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 !]

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).

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

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.

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 $t_2$: (f) $x(t_2) - x(t_1)$ = area under the $v-t$ curve bounded by the $t$-axis and the dotted line shown.

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

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 woman starts from her home at 9.00 am, walks with a speed of $5 km h^{-1}$ on a straight road up to her office $2.5 km$ away, stays at the office up to 5.00 pm, and returns home by an auto with a speed of $25 km h^{-1}$. Choose suitable scales and plot the $x-t$ graph of her motion.

Two trains $A$ and $B$ of length $400 m$ each are moving on two parallel tracks with a uniform speed of $72 km h^{-1}$ in the same direction, with $A$ ahead of $B$. The driver of $B$ decides to overtake $A$ and accelerates by $1 m s^{-2}$. If after $50 s$, the guard of $B$ just brushes past the driver of $A$, what was the original distance between them ?

Read each statement below carefully and state with reasons and examples, if it is true or false ; A particle in one-dimensional motion (d) with positive value of acceleration must be speeding up.

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 ?

In which of the following examples of motion, can the body be considered approximately a point object: (c) a spinning cricket ball that turns sharply on hitting the ground.

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,

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 ?.

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 $t = 0.3 s$, $1.2 s$, $– 1.2 s$.

                                

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

In which of the following examples of motion, can the body be considered approximately a point object: (d) a tumbling beaker that has slipped off the edge of a table.

A boy standing on a stationary lift (open from above) throws a ball upwards with the maximum initial speed he can, equal to $49 m s^{-1}$. How much time does the ball take to return to his hands? If the lift starts moving up with a uniform speed of $5 m s^{-1}$ and the boy again throws the ball up with the maximum speed he can, how long does the ball take to return to his hands ?

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 (b) speed of the child running opposite to the direction of motion of the belt ?

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;