Question

The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with an acceleration of 25.60 m/s2 for 4.20 s, making straight skid marks 62.4 m long, all the way to the tree. With what speed does the car then strike the tree?

Answer 1

For this problem, we use the formula for rectilinear motion at constant acceleration. The equations are:

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

62.4 m = (v₀)(4.20 s) + 0.5(-25.60 m/s²)(4.20 s)²
v₀ = 68.617 m/s

-25.60 m/s² = (v - 68.617 m/s)/4.20 s
v = 38.9 m/s