Answer in Mechanics | Relativity for Quanda #126957

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.

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