Question

A car is traveling to the right with a speed of 2.0\,\dfrac{\text m}{\text s}2.0 s m ​ 2, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction on an icy road when the brakes are applied. The car slows down with constant acceleration for 3.0\,\text m3.0m3, point, 0, start text, m, end text until it comes to a stop. How long does it take the car to slide to a stop?

Answer 1

It took the car 3 second to come to full stop

Step-by-step explanation:

When the car is driving to the right at a speed of 2 m/s, and suddenly brakes giving the car a constant negative acceleration making it travel 3 meters after it stops, we can use the following kinematic equation to solve for the acceleration applied by the brakes:

`v=v_0-a\,t\\0=2-a\,t\\a=(2)/(t)`

and we use this result in the following kinematic equation for the distance traveled to find the time it took it to stop:

`x-x_0=v_0\,t-(1)/(2) a\,\,t^2\\3=2\,t -(1)/(2) ((2)/(t)) \,\,t^2\\3=2\,t-t\\3=t`

therefore, it took the car 3 seconds to come to a full stop.