Question

a police officer finds 60 m of skid marks at the scene of a car crash. Assuming a uniform deceleration of 7.5 m/s to a stop , what was the velocity of the car when it started skidding?

Answer 1

The equation to be used is for the rectilinear motion at constant acceleration:

x = v₀t + 0.5at²
a = (v-v₀)/t
where
x is distance
v and v₀ is the final and initial velocity
t is time
a is acceleration

Because the acceleration is decelerating, that would be reported as -7.5 m/s². Substituting,

-7.5 = (0 - v₀)/t
v₀ = 7.5 t --> eqn 1

x = v₀t + 0.5at²
60 = (7.5t)(t) + 0.5(-7.5)(t²)
Solving for t,
t = 4s

Thus,
v₀ = 7.5 m/s² * 4s
v₀ = 30 m/s