Answer to Question #126957 in Mechanics | Relativity for Quanda

Question #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.


1
Expert's answer
2020-07-23T08:46:22-0400

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


v(t)=v0+atv(t) = v_0 + at

where v0=0v_0 = 0 is the initial velocity (starting from the rest). Thus, we obtain the linear function


v(t)=atv(t) = at

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


d=at22d = \dfrac{at^2}{2}

Expressing aa and substituting the numerical values, obtain:


a=2dt2=200m152s20.89m/s2a = \dfrac{2d}{t^2} = \dfrac{200m}{15^2s^2} \approx 0.89 m/s^2

Thus, obtain the following velocity-time function:


v(t)=0.89tv(t) = 0.89t


and the following graph




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