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 ; (b) (A/B) starts from the school earlier than (B/A)

A player throws a ball upwards with an initial speed of $29.4 m s^{-1}$. (b) What are the velocity and acceleration of the ball at the highest point of its motion ?

Two towns $A$ and $B$ are connected by a regular bus service with a bus leaving in either direction every $T$ minutes. A man cycling with a speed of $20 km h^{-1}$ in the direction $A$ to $B$ notices that a bus goes past him every $18 min$ in the direction of his motion, and every $6 min$ in the opposite direction. What is the period $T$ of the bus service and with what speed (assumed constant) do the buses ply on the road?

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)

A three-wheeler starts from rest, accelerates uniformly with $1 m s^{-2}$ on a straight road for $10 s$, and then moves with uniform velocity. Plot the distance covered by the vehicle during the nth second ($n$ = 1,2,3….) versus $n$. What do you expect this plot to be during accelerated motion : a straight line or a parabola ?

Figure 3.24 gives the $x-t$ plot of a particle in one-dimensional motion. Three different equal intervals of time are shown. In which interval is the average speed greatest, and in which is it the least ? Give the sign of average velocity for each interval.

A player throws a ball upwards with an initial speed of $29.4 m s^{-1}$. (c) Choose the $x = 0 m$ and $t = 0 s$ 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 position, velocity and acceleration of the ball during its upward, and downward motion.

On a two-lane road, car A is travelling with a speed of $36 km h^{-1}$. Two cars $B$ and $C$ approach car $A$ in opposite directions with a speed of $54 km h^{-1}$ each. At a certain instant, when the distance $AB$ is equal to $AC$, both being $1 km$, $B$ decides to overtake $A$ before $C$ does. What minimum acceleration of car $B$ is required to avoid an accident ?

The speed-time graph of a particle moving along a fixed direction is shown in Fig. 3.28. What is the average speed of the particle over the interval in (a) $t = 0 s$ to $10 s$?

Figure 3.23 gives the $x-t$ plot of a particle executing one-dimensional simple harmonic motion. (You will learn about this motion in more detail in Chapter14). Give the signs of position, velocity and acceleration variables of the particle at $t = 0.3 s$, $1.2 s$, $– 1.2 s$.

                                

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 ; (e) (A/B) overtakes (B/A) on the road (once/twice).

A man walks on a straight road from his home to a market $2.5 km$ away with a speed of $5 km h^{-1}$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5 km h^{-1}$. What is the (b) average speed of the man over the interval of time (i) 0 to 30 min

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 $t < 0$ and on a parabolic path for $t > 0$ ? If not, suggest a suitable physical context for this graph.

A man walks on a straight road from his home to a market $2.5 km$ away with a speed of $5 km h^{-1}$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5 km h^{-1}$. What is the (b) average speed of the man over the interval of time (ii) 0 to 50 min

On a long horizontally moving belt (Fig. 3.26), a child runs to and fro with a speed $9 km h^{-1}$ (with respect to the belt) between his father and mother located $50 m$ apart on the moving belt. The belt moves with a speed of $4 km h^{-1}$. For an observer on a stationary platform outside, what is the (c) time taken by the child in (a) speed of the child running in the direction of motion of the belt ? and (b) speed of the child running opposite to the direction of motion of the belt ? Which of the answers alter if motion is viewed by one of the parents ?

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 $t_1$ to $t_2$: (a) $x(t_2) = x(t_1) + v(t_1) (t_2 - t_1) +(\frac{1}{2}) a (t_2 - t_1)^2$

A man walks on a straight road from his home to a market $2.5 km$ away with a speed of $5 km h^{-1}$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5 km h^{-1}$. What is the (a) magnitude of average velocity of the man over the interval of time (ii) 0 to 50 min

A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is $1 m$ long and requires $1 s$. Plot the $x-t$ graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit $13 m$ away from the start.

Two stones are thrown up simultaneously from the edge of a cliff $200 m$ high with initial speeds of $15 m s^{-1}$ and $30 m s^{-1}$. Verify that the graph shown in Fig. 3.27 correctly represents the time variation of the relative position of the second stone with respect to the first. Neglect air resistance and assume that the stones do not rebound after hitting the ground. Take $g = 10 m s^{-2}$. Give the equations for the linear and curved parts of the plot.

A man walks on a straight road from his home to a market $2.5 km$ away with a speed of $5 km h^{-1}$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5 km h^{-1}$. What is the (a) magnitude of average velocity of the man over the interval of time (iii) 0 to 40 min ?