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

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

Step-by-step explanation:

Stage 1: The car moves at constant speed
`v_(i)=25(m)/(s)`.

Stage 2: the car accelerates with
`a=-1.5(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^(*)=(-v_(0))/(a)` ⇒
`t^(*)=16.66s`.