Question

A world-class sprinter can reach a top speed of about 11.5 m/s in the first 25.0 m of a race. Assume his acceleration is a constant. a) What is the acceleration of this sprinter? b) How long does it take him to reach that speed?

Answer 1

a) To find the acceleration of the sprinter, you can use the following formula:

Acceleration (a) = Change in Velocity (Δv) / Time (t)

In this case, the sprinter starts from rest and reaches a top speed of 11.5 m/s. So, the change in velocity is:

Δv = 11.5 m/s - 0 m/s = 11.5 m/s

The time it takes to reach this speed is given as 25.0 seconds.

Now, plug these values into the formula:

Acceleration (a) = Δv / t
Acceleration (a) = 11.5 m/s / 25.0 s

Calculate the acceleration:

a = 0.46 m/s²

b) To find how long it takes for the sprinter to reach a speed of 11.5 m/s, you can use the following formula:

Time (t) = Change in Velocity (Δv) / Acceleration (a)

We already know Δv is 11.5 m/s, and we calculated the acceleration (a) as 0.46 m/s² in part a.

Plug these values into the formula:

Time (t) = 11.5 m/s / 0.46 m/s²

Calculate the time:

t = 25 seconds

So, it takes the sprinter 25 seconds to reach a top speed of 11.5 m/s.