Things work out best for those who make the best of how things work out. – **John Wooden**

# Lecture 12 Motion in a straight line

**Question 3.13** 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 second quantity is either greater than or equal to the first. When is the equality sign true ? For simplicity, consider one-dimensional motion only.

**Question 3.14** 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, and

(b) average speed of the man over the interval of time

(i) 0 to 30 min,

(ii) 0 to 50 min,

(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 !

**Question 3.15** In Exercises 3.13 and 3.14, we have carefully distinguished between average speed and magnitude of average velocity. No such distinction is necessary when we consider instantaneous speed and magnitude of velocity. The instantaneous speed is always equal to the magnitude of instantaneous velocity. Why ?

**Question 3.16** 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 3.17** 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.

**Question 3.18** A police van moving on a highway with a speed of 30 km h^{–1} fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km h^{–1} the muzzle speed of the bullet is 150 m s^{–1} , with what speed does the bullet hit the thief’s car ? Note: Obtain that speed which is relevant for damaging the thief’s car

**Question 3.19** Suggest a suitable physical situation for each of the following graphs:

**Question 3.20** 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.

**Question 3.21** 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.

**Question 3.22** 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 ?