The driver of a truck slams on the brakes when he sees a tree blocking the road. The truck slows down uniformly with acceleration
−5.15 m/s2 for 4.20 s, making skid marks 62.1 m long that end at the tree. With what speed does the truck then strike the tree?
To find the speed at which the truck strikes the tree, we can use kinematic equations of motion. We can start by using the following equation:
v^2 = u^2 + 2as
Where:
v = final velocity (which is what we want to find)
u = initial velocity (which is assumed to be 0 since the truck starts from rest)
a = acceleration = -5.15 m/s^2 (negative because it is deceleration)
s = displacement = 62.1 m
Now we can substitute the values into the equation:
v^2 = 0^2 + 2(-5.15 m/s^2)(62.1 m)
Simplifying the equation gives us:
v^2 = -2(5.15 m/s^2)(62.1 m)
v^2 = -635.3135
Since velocity cannot be negative, we discard the negative sign:
v^2 = 635.3135
Now we take the square root of both sides to find the velocity:
v ≈ √635.3135
v ≈ 25.2 m/s
Therefore, the truck strikes the tree with a speed of approximately 25.2 m/s.