A cyclist is riding along at a constant velocity of 15 m/s. He then accelerates at a uniform rate of 0.50 m/s over a distance of

Question

3 years ago

14

64m. How long did he accelerate for?

1 answer:

VashaNatasha [74] · Answer 1 · 2022-03-31T23:55:48+03:00

The cyclist accelerates for 4 seconds.

Explanation:

The motion of the cyclist is a motion at constant acceleration, so we can use suvat equations:

$s=ut+\frac{1}{2}at^2$

where

s = 64 m is the distance covered

u = 15 m/s is the initial velocity

t is the time

$a=0.50 m/s^2$ is the acceleration

Substituting into the equation,

$64=15t+\frac{1}{2}(0.50)t^2\\0.25t^2+15t-64=0$

Solving the equation for t,

$t=\frac{-15\pm \sqrt{(15)^2-4(0.25)(-64)}}{2(0.25)}$

Which gives two solution: one is negative, so we discarde it since it has no physical meaning; the other one is

t = 4 s

which is the answer we were looking for.

Learn more about accelerated motion:

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