Question

Police lieutenants, examining the scene of an accident involving two cars, measure the skid marks of one of the cars, which nearly came to a stop before colliding, to be 78 m long. The coefficient of kinetic friction between rubber and the pavement is about 0.90. Estimate the initial speed of that car assuming a level road.

Answer 1

37.11231 m/s

Step-by-step explanation:

u = Initial velocity

v = Final velocity = 0

s = Displacement = 78 m

g = Acceleration due to gravity = 9.81 m/s²

`\mu` = Coefficient of kinetic friction = 0.9

Acceleration is given by

`a=-(f)/(m)\\\Rightarrow a=-(\mu mg)/(m)\\\Rightarrow a=-\mu g`

Equation of motion

`v^2-u^2=2as\\\Rightarrow v^2-u^2=-2\mu gs\\\Rightarrow -u^2=2(-\mu g)s-v^2\\\Rightarrow u=√(v^2-2(-\mu g)s)\\\Rightarrow u=√(0^2-2* (-0.9* 9.81)* 78)\\\Rightarrow u=37.11231\ m/s`

The initial speed of that car is 37.11231 m/s