Question

A sprinter in a race accelerates from rest at 1 m/s^2 for 10 s. She then continues east at her final speed for 45 s. How far does the sprinter run?

Answer 1

Distance traveled is given as the product of speed and time.
Acceleration describes how much speed increases each unit of time.

In this case, 1 m/s^2 means the velocity of the sprinter increases 1 m/s every second.
This happens for 10 seconds.

So at the end of 10 seconds, the sprinter is now traveling (1) * (10) = 10 m/s

To find the distance traveled during acceleration: Vf^2 = Vi^2 + 2a(Xf - Xi)
10^2 = 0 + 2(1)(Xf - 0)
100 = 2 Xf
Xf = 50 m

Now the sprinter continues for 45 seconds at this pace.
x = (10) * (45) = 450 m

So combined, the sprinter goes 50+450 = 500 m