Read each statement below carefully and state with reasons and examples, if it is true or false ; A particle in one-dimensional motion (b) with zero speed may have non-zero velocity,

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 $10 s$?

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 ; (c) (A/B) walks faster than (B/A)

Read each statement below carefully and state with reasons and examples, if it is true or false ; A particle in one-dimensional motion (c) with constant speed must have zero acceleration,

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.

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)

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 (b) $t = 2 s$ to $6 s$?

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 $t_2$: (e) $x(t_2) = x(t_1) + v_{average} (t_2 - t_1) + (\frac{1}{2}) a_{average} (t_2 - t_1)^2$

When we consider instantaneous speed and magnitude of velocity. The instantaneous speed is always equal to the magnitude of instantaneous velocity. Why ?

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?

Figure 3.25 gives a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude ? In which interval is the average speed greatest ? Choosing the positive direction as the constant direction of motion, give the signs of $v$ and $a$ in the three intervals. What are the accelerations at the points $A$, $B$, $C$ and $D$ ?

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.

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 $t_2$: (d) $a_{average} = \frac{v(t_2) - v(t_1)}{t_2 - t_1}$

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 (iii) 0 to 40 min ? [Note: You will appreciate from this exercise why it is better to define average speed as total path length divided by time, and not as magnitude of average velocity. You would not like to tell the tired man on his return home that his average speed was zero !]

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 (a) speed of the child running in the direction of motion of the belt ?.

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 (i) 0 to 30 min

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 ?

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 (b) $t = 2 s$ to $6 s$.

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

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