Question

A car is travelling at a constant speed until the car’s brakes are applied. The car’s speed changes at a rate given by -0.08t ms^{-2} after the brakes are applied, where t s is the time since the brakes were applied. 3 seconds after the brakes are applied, the speed of the car is 5 ms^{-1} . How far will the car travel with the brakes applied before it stops?

Answer 1

The car will travel a distance of 52.08 seconds will the brakes applied before it stops

The acceleration of the car after t seconds that the brake was applied is given as:

$a=-0.08t m/s^2$

The speed of the car after  3 seconds that the brake was applied, u = 5 m/s

The speed of the car when it eventually stops, v = 0m/s

3 seconds after the brake was applied:

The time, t = 3 seconds

substitute t = 3 into the acceleration  $a=-0.08t m/s^2$

$a=-0.08(3)m/s^2\\\\a = -0.24m/s^2$

To calculate the distance traveled by the car after the brakes are applied, use the equation below

$v^2=u^2+2as$

Substitute u = 5, a = -0.24, and v = 0 into the equation above in order to calculate the distance

$0^2=5^2+2(-0.24)s\\\\0=25-0.48s\\\\0.48s = 25\\\\s = \frac{25}{0.48}\\\\s = 52.08 m$

The car will travel a distance of 52.08 seconds will the brakes applied before it stops

Learn more here: https://brainly.com/question/25597363