## The velocity-time graph of a particle in one-dimensional

[question] Question. The velocity-time graph of a particle in one-dimensional motion is shown in Fig. 3.29: Which of the following formulae are correct for describing the motion of the particle over the time-interval $t_{2}$ to $t_{1}$ ? (a) $x\left(t_{2}\right)=x\left(t_{1}\right)+v\left(t_{1}\right)\left(t_{2}-t_{1}\right)+\left(\frac{1}{2}\right) a\left(t_{2}-t_{1}\right)^{2}$ (b) $v\left(t_{2}\right)=v\left(t_{1}\right)+a\left(t_{2}-t_{1}\right)$ (c) $v_{\text {Average }}=\left(x\left(t_{2}\...

## The speed-time graph of a particle moving along a fixed direction is

[question] Question. The speed-time graph of a particle moving along a fixed direction is shown in Fig. 3.28. Obtain the distance traversed by the particle between (a) $t=0$ s to $10 \mathrm{~s}$, (b) $t=2 \mathrm{~s}$ to 6 [/question] [solution] solution: (a) Distance travelled by the particle = Area under the given graph $=\frac{1}{2} \times(10-0) \times(12-0)=60 \mathrm{~m}$ Average speed $=\frac{\text { Distance }}{\text { Time }}=\frac{60}{10}=6 \mathrm{~m} / \mathrm{s}$ (b) Let $s_{1}$ and...

## Suggest a suitable physical situation for each of the following graphs

[question] Question. Suggest a suitable physical situation for each of the following graphs [/question] [solution] solution: (a) The given $x-t$ graph shows that initially a body was at rest. Then, its velocity increases with time and attains an instantaneous constant value. The velocity then reduces to zero with an increase in time. Then, its velocity increases with time in the opposite direction and acquires a constant value. A similar physical situation arises when a football (initially kept ...

## Figure $3.21$ shows the $x-t$ plot of one-dimensional motion of a particle.

[question] Question. Figure $3.21$ shows the $x-t$ plot of one-dimensional motion of a particle. Is it correct to say from the graph that the particle moves in a straight line for $t0$ ? If not, suggest a suitable physical context for this graph. [/question] [solution] solution: The $x-t$ graph of a particle moving in a straight line for $t0$ cannot be shown as the given graph. This is because, the given particle does not follow the trajectory of path followed by the particle as $t=0, x=0$. A ph...

## Look at the graphs (a) to (d) (Fig. 3.20) carefully and state,

[question] Question. Look at the graphs (a) to (d) (Fig. 3.20) carefully and state, with reasons, which of these cannot possibly represent one-dimensional motion of a particle. [/question] [solution] solution: (a) The given $x-t$ graph, shown in (a), does not represent one-dimensional motion of the particle. This is because a particle cannot have two positions at the same instant of time. (b) The given $v-t$ graph, shown in (b), does not represent one-dimensional motion of the particle. This is ...

## Explain clearly, with examples, the distinction between:

[question] Question. Explain clearly, with examples, the distinction between: (a) magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval; (b) magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the se...

## A ball is dropped from a height of 90 m on a floor.

[question] Question. A ball is dropped from a height of $90 \mathrm{~m}$ on a floor. At each collision with the floor, the ball loses one tenth of its speed. Plot the speed-time graph of its motion between $t=0$ to $12 \mathrm{~s} .$ [/question] [solution] solution: Ball is dropped from a height, s = 90 m Initial velocity of the ball, $u=0$ Acceleration, $a=g=9.8 \mathrm{~m} / \mathrm{s}^{2}$ Final velocity of the ball $=v$ From second equation of motion, time $(t)$ taken by the ball to hit the ...

## Read each statement below carefully and state with reasons and examples,

[question] Question. Read each statement below carefully and state with reasons and examples, if it is true or false; A particle in one-dimensional motion (a) with zero speed at an instant may have non-zero acceleration at that instant (b) with zero speed may have non-zero velocity, (c) with constant speed must have zero acceleration, (d) with positive value of acceleration mustbe speeding up. [/question] [solution] solution: Answer: (a) True (b) False (c) True (d) False Explanation: (a) When an...

## A player throws a ball upwards with an initial speed of $29.4 \mathrm{~m} \mathrm{~s}^{-1}$.

[question] Question. A player throws a ball upwards with an initial speed of $29.4 \mathrm{~m} \mathrm{~s}^{-1}$. (a) What is the direction of acceleration during the upward motion of the ball? (b) What are the velocity and acceleration of the ball at the highest point of its motion? (c) Choose the $x=0 \mathrm{~m}$ and $t=0 \mathrm{~s}$ to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of $x$-axis, and give the signs of posi...

## The position-time $(x-t)$ graphs for two children $A$ and $B$

[question] Question. The position-time $(x-t)$ graphs for two children $A$ and $B$ returning from their school $O$ to their homes $P$ and $Q$ respectively are shown in Fig. 3.19. Choose the correct entries in the brackets below; (a) (A/B) lives closer to the school than (B/A) (b) (A/B) starts from the school earlier than (B/A) (c) (A/B) walks faster than (B/A) (d) A and B reach home at the (same/different) time (e) (A/B) overtakes (B/A) on the road (once/twice). [/question] [solution] solution: ...

## In which of the following examples of motion,

[question] Question. In which of the following examples of motion, can the body be considered approximately a point object: (a) a railway carriage moving without jerks between two stations. (b) a monkey sitting on top of a man cycling smoothly on a circular track. (c) a spinning cricket ball that turns sharply on hitting the ground. (d) a tumbling beaker that has slipped off the edge of a table. [/question] [solution] solution: Answer: (a), (b) (a) The size of a carriage is very small as compare...