Describing Motion Around Us — Class 9 Science
Exploration · Chapter 4
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Chapter summary
Key ideas & terms
- Distance
- The total length of the path actually covered by a moving object; a scalar with magnitude only.
- Displacement
- The shortest straight-line change in position, from initial to final point; a vector with magnitude and direction.
- Velocity
- The displacement of an object per unit time; a vector that tells both how fast and in which direction it moves.
- Acceleration
- The rate of change of velocity with time,
, measured in . - Equations of motion
- For uniform acceleration:
, , and . - Uniform circular motion
- Motion along a circle at constant speed; the velocity keeps changing direction, so the motion is accelerated.
Extra questions & answers
Differentiate distance and displacement.
Distance is the whole path length covered and is a scalar; displacement is the shortest straight-line gap between start and end positions and is a vector, so it can be zero even when distance is large (e.g. returning to the starting point).
How are speed and velocity different?
Speed is
Define acceleration and give its SI unit.
Acceleration is the rate of change of velocity with time,
What does negative acceleration mean?
It means the velocity is decreasing with time, i.e. the object is slowing down; this is also called retardation or deceleration.
Write the three equations of motion for uniform acceleration.
They are
What does the slope of a distance-time graph represent?
It represents the speed of the object; a steeper slope means a higher speed and a horizontal line means the object is at rest.
What information do you get from a velocity-time graph?
The slope gives the acceleration, and the area enclosed between the line and the time axis gives the distance travelled by the object.
A car starts from rest and reaches
Using
Why is uniform circular motion said to be accelerated even at constant speed?
Because the direction of motion changes continuously around the circle, the velocity (a vector) changes continuously, and any change in velocity means acceleration, even though the speed is constant.
Give two everyday examples of uniform circular motion.
A stone tied to a string and whirled steadily in a circle, and the Moon revolving around the Earth, are both examples of uniform circular motion.
Think It Over
How much distance should we maintain from the truck ahead to avoid a collision if it suddenly applies the brakes?
The safe distance is the total stopping distance, which is the distance covered during the driver's reaction time plus the braking distance. If the truck brakes suddenly, our vehicle continues to move for the reaction time
Does this distance depend upon the speed with which we are moving?
Yes. Both the reaction distance
Activity 4.1: Let us analyse
1. As shown in Fig. 4.5, a ball is thrown vertically upwards from O. It moves up straight till B and then falls back to O. Can this be considered a motion in a straight line?
Yes. Although the ball goes up and then comes down, its trajectory is along the same vertical straight line. The motion is one-dimensional. The use of two separate lines in the figure is only for clarity; displacement and distance are measured along the same line with upward as positive and downward as negative or vice versa.
2. For this motion, fill up the values in Table 4.1. Table 4.1: Distance travelled and displacement of the ball S. No. Position Total distance travelled by the ball from O till that position Displacement of the ball from O till that position 1. O 0 cm 0 cm 2. A 40 cm 40 cm in upward direction 3. B 4. C 5. O
Taking upward as positive and
3. Analyse the data filled in Table 4.1 and choose which of the following is true for displacement: (i) It is never zero.
False. As seen in the table, when the ball returns to
3. Analyse the data filled in Table 4.1 and choose which of the following is true for displacement: (ii) Its magnitude can be greater than the total distance travelled.
False. From the table the magnitude of displacement is
3. Analyse the data filled in Table 4.1 and choose which of the following is true for displacement: (iii) Its magnitude is less than or equal to the total distance travelled.
True. In all cases observed
3. Analyse the data filled in Table 4.1 and choose which of the following is true for displacement: (iv) Its magnitude is less than the total distance travelled in all cases.
False. While moving in one direction before turning back, e.g.,
Pause and Ponder
1. In the example of an athlete running back and forth on a straight track (Fig. 4.4), when will the displacement of the athlete be zero? What will be the total distance travelled in that case?
Displacement is the change from the initial position
2. Fuel used up in a vehicle depends on which of the following? Justify your answer. (i) Total distance travelled
Fuel consumption depends on total distance travelled. Work done against friction and engine effort is proportional to the actual path length covered, not the net change in position. Even if the vehicle returns to the start and displacement is zero, fuel has been burnt for the whole journey.
2. Fuel used up in a vehicle depends on which of the following? Justify your answer. (ii) Displacement
Displacement alone does not determine fuel use. Two trips can have the same displacement (including zero) but very different path lengths and hence different fuel consumption. Therefore fuel used is not a function of displacement.
3. A ball rolls down an inclined track as shown in Fig. 4.6. Is its motion, a straight line motion? Assuming the starting point of the ball (O) to be the origin, can its motion from O to D be depicted using a horizontal line as shown in Fig. 4.3? Are the values of total distance travelled and magnitude of displacement from O equal or different at positions A, B, C and D?
Yes, the inclined track is straight, so motion is in a straight line, only inclined to the horizontal. It can be represented on a one-dimensional axis along the incline; for convenience we can draw it as a horizontal line with
4. During a family road trip, you drive 200 km north in three hours. Afterwards, you drive 200 km south in two hours. Find the average speed and average velocity for your entire trip.
Total distance
5. Under what condition(s) is the (i) magnitude of average velocity of an object equal to its average speed?
When the object moves in a straight line in one direction without turning back during the time interval. Then
5. Under what condition(s) is the (ii) magnitude of average velocity of an object zero while its average speed is not zero?
When the object returns to its starting position so that net displacement is zero but path length is non-zero. Then
Activity 4.2: Let us calculate
1. The magnitude of average acceleration of cars is generally specified as the time taken by the car to go from 0 km h–1 to 100 km h–1. Look it up on the internet and find this time for various cars, and record those in Table 4.2.
Example entries (actual values vary by model): Small hatchback
2. Calculate the magnitude of average acceleration for each car. Table 4.2: The magnitude of average acceleration in a time interval Car type Time interval during which the speed goes from 0 to 100 km h–1 Magnitude of average acceleration (m s–2)
Activity 4.5: Let us investigate
1. Take a ring, such as an adhesive tape ring and one marble. 2. Place the ring flat on a smooth surface and throw the marble inside the ring in a way that it rotates along the inner boundary of the ring (Fig. 4.24). 3. Predict what will happen if you lift the ring while the marble is moving. 4. Now, after one or two complete revolutions of the marble, pick up the ring without disturbing the motion of the marble. What do you observe? Does the marble continue moving in a circular motion? Or does it move in some other manner? 5. Repeat the activity multiple times to confirm the result.
Prediction: The marble is constrained to a circle by the ring. When the constraint is removed it will continue in the direction it had at that instant. Observation: On lifting the ring the marble leaves the circular path and moves in a straight line tangent to the circle at the point of release, gradually slowing due to friction. Repeated trials show the same tangential straight-line motion, illustrating that the direction of velocity in uniform circular motion is tangential and that without a centripetal constraint the object moves linearly.
Revise, Reflect, Refine
1. My father went to a shop from home which is located at a distance of 250 m on a straight road. On reaching there, he discovered that he forgot to carry a cloth bag. He came home to take it, went to the shop again, bought provisions and came back home. How much was the total distance travelled by him? What was his displacement from home?
Path: Home
2. A student runs from the ground floor to the fourth floor of a school building to collect a book and then comes down to their classroom on the second floor. If the height of each floor is 3 m, find: (i) the total vertical distance travelled, and
Height of one floor
2. A student runs from the ground floor to the fourth floor of a school building to collect a book and then comes down to their classroom on the second floor. If the height of each floor is 3 m, find: (ii) their displacement from the starting point.
Taking upward as positive and ground as
3. A girl is riding her scooter and finds that its speedometer reading is constant. Is it possible for her scooter to be accelerating and if so, how?
Yes. Speedometer shows magnitude of velocity. Even with constant speed
4. A car starts from rest and its velocity reaches 24 m s–1 in 6 s. Find the average acceleration and the distance travelled in these 6 s.
5. A motorbike moving with initial velocity 28 m s–1 and constant acceleration stops after travelling 98 m. Find the acceleration of the motorbike and the time taken to come to a stop.
6. Fig. 4.27 shows a position-time graph of two objects A and B that are moving along the parallel tracks in the same direction. Do objects A and B ever have equal velocity? Justify your answer.
Velocity is the slope of the position-time graph. If one graph is a straight line and the other is curved, the slope of the curved graph changes with time. Equal velocity occurs at the instant where the tangent to the curved graph is parallel to the straight line. If the figure shows two straight lines with different slopes, they never have equal velocity; if one is curved, there will be a point where the slopes match. In many textbook versions A is straight and B is curved and they intersect but the slopes are equal only where the tangent to B is parallel to A.
7. A graph in Fig. 4.28 shows the change in position with time for two objects A and B moving in a straight line from 0 to 10 seconds. Choose the correct option(s). (i) The average velocity of both over the 10 s time interval is equal since they have the same initial and final positions.
True. Both start at the same position at
7. A graph in Fig. 4.28 shows the change in position with time for two objects A and B moving in a straight line from 0 to 10 seconds. Choose the correct option(s). (ii) The average speeds of both over the 10 s time interval are equal since both cover equal distance in equal time.
False. Average speed depends on total path length, not net displacement. If one object back-tracks, its total distance is larger. The position-time graph for B shows back-and-forth movement, so its total distance is greater than A's monotonic movement.
7. A graph in Fig. 4.28 shows the change in position with time for two objects A and B moving in a straight line from 0 to 10 seconds. Choose the correct option(s). (iii) The average speed of A over the 10 s time interval is lower than that of B since it covers a shorter distance than B in 10 seconds.
True. Object A moves steadily from start to end without reversing, while B goes beyond and returns, covering extra length. Hence distance travelled by B is greater, so average speed of B
7. A graph in Fig. 4.28 shows the change in position with time for two objects A and B moving in a straight line from 0 to 10 seconds. Choose the correct option(s). (iv) The average speed of A over the 10 s time interval is greater than that of B since B’s speed is lower than A’s in some segments.
False. Although B may move slowly in some segments, its total path length over the whole
8. A truck driver driving at the speed of 54 km h–1 notices a road sign with a speed limit of 40 km h–1 (Fig. 4.29) for trucks. He slows down to 36 km h–1 in 36 s. What was the distance travelled by him during this time? Assume the acceleration to be constant while slowing down.
9. A car starts from rest and accelerates uniformly to 20 m s–1 in 5 seconds. It then travels at 20 m s–1 for 10 seconds and finally applies the brake (with uniform acceleration) to stop in 6 seconds. Find the total distance travelled.
Phase 1:
10. A bus is travelling at 36 km h–1 when the driver sees an obstacle 30 m ahead. The driver takes 0.5 seconds to react before pressing the brake. Once the brake is applied, the velocity of the bus reduces with constant acceleration of 2.5 m s–2. Will the bus be able to stop before reaching the obstacle?
11. A student said, “The Earth moves around the Sun”. In this context, discuss whether an object kept on the Earth can be considered to be at rest.
Rest and motion are relative to the reference point. With respect to the Earth's surface, a book on a table does not change position, so it is at rest in the Earth frame. With respect to the Sun or stars, the same book is moving as the Earth orbits at about
12. The velocity-time graph from 0 s to 120 s for a cyclist is shown in Fig. 4.30. Shade the areas (in different colours) representing the displacement of the cyclist (i) while cyclist is moving with constant velocity.
On a velocity-time graph displacement is the area under the curve. The segment where the graph is horizontal, parallel to the time axis, represents constant velocity. Its area is a rectangle:
12. The velocity-time graph from 0 s to 120 s for a cyclist is shown in Fig. 4.30. Shade the areas (in different colours) representing the displacement of the cyclist (ii) when the velocity of cyclist is decreasing.
The segment where the graph slopes downward represents decreasing velocity with negative acceleration. Its area, which is a triangle or trapezium under that sloping line, represents displacement during deceleration and should be shaded with a different colour.
12. The velocity-time graph from 0 s to 120 s for a cyclist is shown in Fig. 4.30. Also, calculate the displacement and average acceleration in the 120 s time interval.
The displacement equals the area under the velocity–time graph (Fig. 4.30). Reading the graph, the velocity rises from 0 to 3 m s
13. A girl is preparing for her first marathon by running on a straight road. She uses a smartwatch to calculate her running speed at different intervals. The graph (Fig. 4.31) depicts her velocity versus time. Estimate the running distance based on the graph.
The distance is the area under the velocity–time graph (Fig. 4.31), where velocity is in km h
14. On entering a state highway, a car continues to move with a constant velocity of 6 m s–1 for 2 minutes and then accelerates with a constant acceleration 1 m s–2 for 6 seconds. Find the displacement of the car on the state highway in the 2 min 6 s time interval by drawing a velocity-time graph for its motion.
Draw time on x-axis and velocity on y-axis. For
15. Two cars A and B start moving with a constant acceleration from rest in a straight line. Car A attains a velocity of 5 m s–1 in 5 s. Car B attains a velocity of 3 m s–1 in 10 s. Plot the velocity-time graphs for both the cars in the same graph. Using the graph, calculate the displacement mentioned in the two time intervals (Hint: Calculate the acceleration in both cases. Then calculate their velocities at five instants of time to plot the graph).
16. Rohan studies science from 6 PM to 7:30 PM at home. Consider the tip of the minute’s hand of the wall clock. During the given time interval, what is its: (i) distance travelled,
Time interval
16. Rohan studies science from 6 PM to 7:30 PM at home. Consider the tip of the minute’s hand of the wall clock. During the given time interval, what is its: (ii) displacement,
At
16. Rohan studies science from 6 PM to 7:30 PM at home. Consider the tip of the minute’s hand of the wall clock. During the given time interval, what is its: (iii) speed, and
Average speed
16. Rohan studies science from 6 PM to 7:30 PM at home. Consider the tip of the minute’s hand of the wall clock. During the given time interval, what is its: (iv) velocity. The length of the minute’s hand is 7 cm (Fig. 4.32).
Average velocity
The Journey Beyond
Take a cardboard disc (radius ~ 8 cm) (Fig. 4.33). Write numbers 1 to 12 on the outer part (7 cm from the centre) and the letters ‘ABCDEF’ on the inner part (4 cm from the centre), using the same font size. Spin the disc slowly, then faster and observe how the numbers and letters appear. Why do the numbers fade or disappear while the letters remain visible? Are the speeds of the numbers and letters the same or different? Justify your answer.
When the disc rotates with angular velocity
Many smartphones have an inbuilt accelerometer that can detect very small accelerations. Install an app, such as Phyphox (phyphox.org) and open ‘Accelerometer (without g)’. Note the readings when (i) the phone is on an outstretched palm, and (ii) the phone is kept on the floor. What differences do you observe? What does this tell you about motion and acceleration in real situations? (Such tiny, involuntary movements are also studied in medical research, for example, in movement disorders) This activity is recommended to be performed as a classroom group activity facilitated by teacher.
On the palm the accelerometer shows small fluctuating accelerations of order
For motion in a straight line with constant acceleration, we derived two primary equations given by Eq. (4.4a) and (4.4b). Using these two equations, three more equations can be derived, out of which we derived one given in Eq. (4.4c). Derive the remaining two equations given below s = vt - 1/2 at^2 s = 1/2 (u+v)t In mathematics, you have learnt the formula for calculating the area of a trapezium. Using that formula, derive the second equation given above.
From
Plot graphs for data given in Table 4.4, using different X and Y scales, on different graph papers. Compare the graphs to find how the appearance of graph is affected by the choice of scales and decide which scale is better and why. Now repeat this with any graph plotting app. Such apps generally automatically adjust the axes to fit the data well on the screen.
Changing scales stretches or compresses axes: a small scale on the x-axis makes the curve look steeper, a large scale makes it flatter, but the physical slope
Talk to a motor mechanic about how a vehicle’s braking or stopping distance is affected by: (i) wet roads, (ii) worn-out tyres, (iii) higher vehicle mass, (iv) driving at night, (v) fog, (vi) severe weather (rain, snow, storm), and (vii) driver reaction time. Using this information, design safety posters for your school and prepare a short skit to present it in the assembly.
Key points: wet or icy roads reduce friction so deceleration