Question

To pass a physical fitness test, massimo must run 1250 m at an average rate of 2.0 m/s. He runs the first 1150 m in 500 s. Can he pass the test? If so, determine at least how fast he must run the last 100 m.

Answer 1

If he runs the first 1150 m in 500 s he will pass the test.

He need to run remaining 100 m at 0.8 m/s to pass the test

Step-by-step explanation:

We know the equation of motion
`s = ut+(1)/(2) at^2`, where s is the displacement, u is the initial velocity, t is the time taken and a is the acceleration.

When he runs 1150 m in 500 s, s = 1150 m, t = 500 s and a = 0
`m/s^2`.

Substituting

`1150 = u*500+(1)/(2) *0*500^2\\ \\ u = 2.3 m/s`

So his speed is more than 2 m/s, so he can pass the test.

If massimo is covering 1250 m at an average rate of 2.0 m/s, time taken by him.

`1250 = 2*t+(1)/(2) *0*t^2\\ \\ t = 625 s`

So he need to cover remaining 100 m in (625-500) = 125 seconds.

Speed required = Distance /Time = 100/125 = 0.8 m/s.

So he need to run remaining 100 m at 0.8 m/s to pass the test.