Question

A person driving a car suddenly applies the brakes. The car takes 4 s to come to rest while traveling 20 m at constant acceleration. Can the speed of the car immediately before the brakes were applied be determined without first determining the car’s acceleration?

Answer 1

Answer:

Yes we can find the initial velocity of car without finding acceleration.

u = 10 m/s.

Explanation:

Given that

s=20 m

Car takes 4 s to come in rest.

We know that when acceleration is constant then we can apply motion equation

$v=u+at$        ----------1

$s=ut+\dfrac{1}{2}at^2$       ------2

From equation 1 and 2

$s=ut+\dfrac{1}{2}t^2\left (\dfrac{v-u}{t} \right )$

So we can say that

$s= \left(\dfrac{v+u}{2}\right)t$

Given that the velocity of car at final condition will be zero (v=0)

$s= \left(\dfrac{0+u}{2}\right)t$

$s= \left(\dfrac{u}{2}\right)t$

From the above equation we can find the initial velocity of car without finding the acceleration

$20= \dfrac{u}{2}\times 4$

u = 10 m/s