In coming to a stop, a car leaves skid marks 88 m long on the highway. Assuming a deceleration of 7.50 m/s2, estimate the speed of the car just before braking.
Physics
Phyics
To estimate the speed of the car just before braking, we can make use of the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (unknown)
u = initial velocity (speed of the car just before braking)
a = acceleration (deceleration in this case)
s = distance traveled (length of the skid marks)
Rearranging the equation, we get:
v^2 = u^2 + 2as
Since we want to find the initial velocity (u), we can isolate it:
u^2 = v^2 - 2as
Now we can substitute the given values:
u^2 = 0 (since the car comes to a stop)
s = 88 meters
a = -7.50 m/s^2 (negative sign because it's a deceleration)
Plugging these values into the equation, we can solve for u:
u^2 = 0 - 2(-7.50)(88)
u^2 = 0 + 2(7.50)(88)
u^2 = 2(7.50)(88)
u^2 = 1056
Finally, taking the square root of both sides we find:
u = √1056
Using a calculator, we can calculate the square root of 1056:
u ≈ 32.5 m/s
Therefore, the estimated speed of the car just before braking is approximately 32.5 m/s.
88 = 1/2 (7.5)t^2
t = 4.84s
v = 7.5*4.84 = 36.3 m/s