Question

The coefficient of static friction between car's tires and a level road is 0.80 If car to be stopped in time of 3.0 sec its speed is

Answer 1

23.5 m/s

Step-by-step explanation:

The velocity of the car in decelerated motion is given by

v = u + at

where

v = 0 is the final velocity

u is the initial velocity

a is the acceleration of the car

t = 3.0 s is the time it takes for the car to stop

The acceleration of the car is given by the frictional force, which is the only force acting on the car along the direction of motion, so:

`ma = -\mu mg\\a = -\mu g = -(0.80)(9.8 m/s^2)=-7.84 m/s^2`

where

`\mu=0.80` is the coefficient of friction

Solving the previous equation for u, we find the initial velocity:

`u=v-at=0-(-7.84 m/s^2)(3.0 s)=23.5 m/s`