Question

a car slows down from 23 m/s to rest in a distance of 85m. what was its acceleration, assumed constant?

Answer 1

u = 23 m/s, initial speed
v = 0, final speed (the car comes to rest)
s = 85 m, distance traveled.

Let a = the acceleration.
Use the formula
u² + 2as = v²
(23 m/s)² + 2*(a m/s²)*(85 m) = 0
529 + 170a =
a = -529/170 = - 3.11 m/s²

Answer: - 3.1 m/s² (this is a deceleration).

Answer 2

In this case, the car slow down from 23m/s into rest which means 0m/s. That mean the average speed of the car would be: (23m/s + 0 ms)/2= 11.5m/s.
If the car moved for 85m with that average speed, then the time car moves would be:
85m/ (11.5m/s)= 7.39s

The car moves for 7.39 second, losing velocity from 23m/s into 0m/s. Then the acceleration would be:
(23m/s - 0m/s)/ 7.39s= 3.11 second