Class 9 › Science › Exploration Describing Motion Around Us Class 9 Science · Exploration · Chapter 4
Summary Questions & answers Practise this chapter → This chapter develops a precise way to describe motion in a straight line and in a circle. Position is given relative to a chosen reference point. Distance is the total path length covered (a scalar, only magnitude), while displacement is the shortest straight-line change in position from start to finish (a vector, having both magnitude and direction); displacement can be zero even when distance is not. Speed is \(\text{speed} = \dfrac{\text{distance}}{\text{time}}\) and is a scalar, whereas velocity is displacement per unit time and is a vector. For changing motion we use average speed and average velocity. Acceleration is the rate of change of velocity, \(a = \dfrac{v - u}{t}\), measured in \(\text{m s}^{-2}\); it is positive when speeding up and negative (retardation) when slowing down. For uniform acceleration the three equations of motion apply: \(v = u + at\), \(s = ut + \tfrac{1}{2}at^2\) and \(v^2 = u^2 + 2as\). Motion can be shown with distance-time graphs (slope gives speed) and velocity-time graphs (slope gives acceleration, and the area under the line gives distance). Finally, in uniform circular motion an object moves around a circle at constant speed, yet because its direction keeps changing its velocity is continuously changing, so it is accelerating; examples include a stone whirled on a string or the Moon orbiting the Earth.
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, \(a = \dfrac{v-u}{t}\), measured in \(\text{m s}^{-2}\).
Equations of motion
For uniform acceleration: \(v = u + at\), \(s = ut + \tfrac{1}{2}at^2\), and \(v^2 = u^2 + 2as\).
Uniform circular motion
Motion along a circle at constant speed; the velocity keeps changing direction, so the motion is accelerated.
Q1 Differentiate distance and displacement. Answer Q2 How are speed and velocity different? Answer Q3 Define acceleration and give its SI unit. Answer Q4 What does negative acceleration mean? Answer Q5 Write the three equations of motion for uniform acceleration. Answer Q6 What does the slope of a distance-time graph represent? Answer Q7 What information do you get from a velocity-time graph? Answer Q8 A car starts from rest and reaches \(20\,\text{m s}^{-1}\) in 5 s. Find its acceleration. Answer Q9 Why is uniform circular motion said to be accelerated even at constant speed? Answer Q10 Give two everyday examples of uniform circular motion. Answer Q1 How much distance should we maintain from the truck ahead to avoid a collision if it suddenly applies the brakes? Answer Q2 Does this distance depend upon the speed with which we are moving? Answer Q1 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? Answer Q2 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 Answer Q3 3. Analyse the data filled in Table 4.1 and choose which of the following is true for displacement: (i) It is never zero. Answer Q4 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. Answer Q5 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. Answer Q6 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. Answer Q1 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? Answer Q2 2. Fuel used up in a vehicle depends on which of the following? Justify your answer. (i) Total distance travelled Answer Q3 2. Fuel used up in a vehicle depends on which of the following? Justify your answer. (ii) Displacement Answer Q4 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? Answer Q5 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. Answer Q6 5. Under what condition(s) is the (i) magnitude of average velocity of an object equal to its average speed? Answer Q7 5. Under what condition(s) is the (ii) magnitude of average velocity of an object zero while its average speed is not zero? Answer Q1 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. Answer Q2 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) Answer Q1 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. Answer Q1 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? Answer Q2 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 Answer Q3 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. Answer Q4 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? Answer Q5 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. Answer Q6 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. Answer Q7 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. Answer Q8 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. Answer Q9 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. Answer Q10 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. Answer Q11 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. Answer Q12 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. Answer Q13 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. Answer Q14 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? Answer Q15 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. Answer Q16 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. Answer Q17 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. Answer Q18 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. Answer Q19 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. Answer Q20 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. Answer Q21 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). Answer Q22 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, Answer Q23 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, Answer Q24 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 Answer Q25 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). Answer Q1 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. Answer Q2 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. Answer Q3 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. Answer Q4 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. Answer Q5 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. Answer
Which quantity is a vector, having both magnitude and direction?
A Time B Displacement C Distance D Speed
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