A driver applies the brakes producing a constant deceleration of 18 feet per second. The car travels 100ft before stopping.

Question

How fast was the car going when the driver hit the brakes

Answer 1

Let

a = 18 ft/s² be the deceleration (not 18 ft/s as given in the statement),

s = 100 ft be the distance traveled,

t be the time before stopping (yet unknown),

v be the initial velocity to be calculated.

From definition of deceleration

v = at

s = at²/2

Therefore

t = sqrt(2s/a)

v = a.sqrt(2s/a) = sqrt(2as)

Substituting given values

v = sqrt(2 . 18 ft/s² . 100 ft)

= sqrt(3600 ft²/s²)

= 60 ft/s