Answer to Question #126957 in Mechanics | Relativity for Quanda

Question

A boy in a 100 m flat race accelerates from rest and completes the race in 15 s. Sketch a velocity-time graph for his motion.

Answer 1

For the constant acceleration $a$ , the velocity as a function of time will be:

$$v(t) = v_0 + at$$

where $v_0 = 0$ is the initial velocity (starting from the rest). Thus, we obtain the linear function

$$v(t) = at$$

Let's find the acceletation. The distance $d$ covered under a constant acceleration is given by:

$$d = \dfrac{at^2}{2}$$

Expressing $a$ and substituting the numerical values, obtain:

$$a = \dfrac{2d}{t^2} = \dfrac{200m}{15^2s^2} \approx 0.89 m/s^2$$

Thus, obtain the following velocity-time function:

$$v(t) = 0.89t$$

and the following graph