What went wrong when the king rode under the arch?

It was too low and knocked off his crown

How does the chain of blame unfold in the poem?

Each accused person blames another, ending with the king's own changes

Define instantaneous velocity.

It is the velocity at a particular instant, defined as \(v=\lim_{\Delta t\to0}\Delta x/\Delta t=\mathrm{d}x/\mathrm{d}t\), equal to the slope of the position-time tangent.

How does average speed compare with the magnitude of average velocity?

Average speed is always greater than or equal to the magnitude of average velocity; they are equal only when motion is along a straight line without reversal.

What does the area under a velocity-time graph represent?

It represents the displacement of the object over the corresponding time interval.

Can a body have zero velocity but non-zero acceleration?

Yes — for example, a ball thrown upward has zero velocity at its highest point but still has acceleration \(g\) downward.

State Galileo's law of odd numbers for free fall.

The distances traversed in successive equal time intervals by a body falling from rest are in the ratio 1:3:5:7..., the odd numbers.

On what does stopping distance of a vehicle depend?

It is proportional to the square of the initial speed and inversely related to the deceleration, so doubling the speed quadruples the stopping distance.

What is reaction time?

The time a person takes to observe, think and act in response to a situation, for example before applying the brakes of a car.

How is acceleration found from a velocity-time graph?

It is the slope of the velocity-time graph at the relevant instant.

Define relative velocity of A with respect to B.

It is \(v_{AB}=v_A-v_B\), the velocity of A as observed from B.

Motion in a Straight Line

Q: Write the three kinematic equations for uniform acceleration.

\(v=v_0+at\); \(x=v_0t+\tfrac12 at^{2}\); and \(v^{2}=v_0^{2}+2ax\).

Class 11 Physics · Physics Part I · Chapter 2

163 members in the CBSE community

View all

CBSE Class 11 · Physics

Every formula of Ch 1–7, with page numbers

Marks booster + cheatsheet: key concepts in 2 lines each, common traps
23-mark block: Ch 1–4
17-mark block: Ch 5–7
Common traps, corrected
7 chapters: every solved-example result
Every unit and dimension, listed

Page 1 free about 8 min read, Full kit about 55 min read

₹159See the full kit

CBSE Class 11 · Physics

Ch 8–14 formulas and table values, by page

Marks booster + cheatsheet: key concepts in 2 lines each, common traps
20-mark block: Ch 8–12
10-mark block: Oscillations and Waves
Common traps, corrected
7 chapters: every solved-example result
Sound, standing waves and beats covered

Page 1 free about 8 min read, Full kit about 55 min read

₹159See the full kit

View all 44 amazing Marks Booster kits →

Summary

This chapter describes rectilinear motion — the motion of an object treated as a point along a straight line — without enquiring into its causes (kinematics). Position is measured from a chosen origin and may be positive or negative. Average velocity is displacement divided by time interval, while instantaneous velocity is the limit of average velocity as the interval shrinks to zero, \(v=\mathrm{d}x/\mathrm{d}t\); graphically it is the slope of the tangent to the position-time graph. Speed is the magnitude of velocity, and average speed (path length over time) is always greater than or equal to the magnitude of average velocity. Acceleration is the rate of change of velocity, \(a=\mathrm{d}v/\mathrm{d}t\), and may be positive, negative or zero. The area under a velocity-time graph equals the displacement. For uniformly accelerated motion the three kinematic equations \(v=v_0+at\), \(x=v_0t+\tfrac12 at^{2}\) and \(v^{2}=v_0^{2}+2ax\) relate displacement, time, initial and final velocities and acceleration, and can be derived graphically or by calculus. Free fall under gravity, with \(a=-g\), is an important special case, illustrated by Galileo's law of odd numbers, stopping distance and reaction time. Relative velocity describes the motion of one object as seen from another.

Instantaneous velocity and speedAccelerationKinematic equations for uniformly accelerated motionVelocity-time and position-time graphsFree fall under gravityRelative velocity in one dimension

Key terms

Instantaneous velocity

The limit of average velocity as the time interval tends to zero, \(v=\mathrm{d}x/\mathrm{d}t\); the slope of the position-time tangent.

Average speed

Total path length divided by the time interval; it is greater than or equal to the magnitude of average velocity.

Acceleration

The rate of change of velocity with time, \(a=\mathrm{d}v/\mathrm{d}t\); it can be positive, negative or zero.

Uniform motion

Motion in which equal displacements occur in equal time intervals, so velocity is constant and acceleration is zero.

Free fall

Motion of a body under gravity alone, with constant downward acceleration \(g\approx9.8\ \text{m s}^{-2}\).

Relative velocity

The velocity of one object with respect to another, equal to the difference of their velocities.

Extra questions & answers

Try one from this chapter

Instantaneous velocity is the slope of the:

Flashcards & interactive practice