Question

A car is traveling at 100 km/h when the driver sees an accident 80 m ahead and slams on the brakes. what minimum constant deceleration is required to stop the car in time to avoid a pileup? (round your answer to two decimal places.)

Answer 1

Assuming the driver starts slamming the brakes immediately, the car moves by uniformly decelerated motion, so we can use the following relationship
$2aS = v_f^2 - v_i^2$ (1)
where 
a is the deleceration
S is the distance covered after a time t
$v_f$ is the velocity at time t
$v_i=100 km/h = 27.8 m/s$ is the initial speed of the car

The accident is 80 m ahead of the car, so the minimum deceleration required to avoid the accident is the value of a such that S=80 m and $v_f=0$ (the car should stop exactly at S=80 m to avoid the accident). Using these data, we can solve  the equation (1) to find a:
$a=- \frac{v_i^2}{2 S}= -\frac{(27.8 m/s)^2}{2 \cdot 80 m} =-4.83 m/s^2$
And the negative sign means it is a deceleration.