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?
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
