Question

Two cars are traveling along a straight line in the same direction, the lead car at 25 m/s and the other car at 38 m/s. At the moment the cars are 45 m apart, the lead driver applies the brakes, causing the car to have a deceleration of 1.5 m/s2 . How long does it take for the lead car to stop?

Answer 1

Answer:

It will take $t=16.66s$ for the lead car to stop.

Explanation:

Stage 1: The car moves at constant speed $v_{i}=25\frac{m}{s}$.

Stage 2: the car accelerates with $a=-1.5\frac{m}{s^{2} }$ (the negative sign means it's decelerating with respect to the direction is moving).

¿When will be the velocity be $v=0$?

From Kinematics: $v(t)=v_{0}+at$

So, if final velocity is $v(t^{*} )=0$

then,

$0=v_{0}+at^{*}$ ⇒ $t^{*}=\frac{-v_{0}}{a}$ ⇒ $t^{*}=16.66s$.