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 -5.60 m/s^2 for 4.20 s, making mark straight skid marks of 62.4 m long ending at the tree. With what speed does the car then strike the tree?
average speed = 62.4 m / 4.20 s = (initial + final) / 2
change in speed = -5.60 m/s^2 * 4.20 s = initial - final
solve the system for final
To find the speed at which the car strikes the tree, we can use the kinematic equation:
π£Β² = π£βΒ² + 2ππ
Where:
π£ = final velocity (speed of the car when it hits the tree)
π£β = initial velocity (initial speed of the car)
π = acceleration
π = distance
In this case, the car starts from rest (π£β = 0), and the acceleration (π) is given as -5.60 m/sΒ². We are given the skid mark distance (π) as 62.4 m.
Substituting the known values into the equation, we have:
π£Β² = 0 + 2(-5.60)(62.4)
Simplifying:
π£Β² = -11.20(-62.4)
π£Β² = 699.84
Taking the square root of both sides, we get:
π£ = β699.84
π£ β 26.45 m/s
Therefore, the car strikes the tree with a speed of approximately 26.45 m/s.