Question

A cyclist is riding along at a constant velocity of 15 m/s. he then accelerates at a uniform rate of 0.50 m/s2 over a distance of 64 m. how long did he accelerate for?

Answer 1

Cyclist will take 4 seconds to travel 64 meter.

Explanation:

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

In this case initial velocity = 15 m/s, acceleration = 0.50
`m/s^2`, we need to calculate time when displacement = 64 meter.

Substituting

`64=15*t+(1)/(2) *0.50*t^2\\ \\ t^2+60t-256=0\\ \\ (t-4)(t+64)=0`

t = 4 seconds or t = -64 seconds(which is not possible).

So he will take 4 seconds to travel 64 meter.