To find the shortest distance in which the car can be stopped, we need to calculate the deceleration of the car and then use the equation for distance with constant acceleration.
Given:
Initial speed, u = 72 km/h
Coefficient of static friction, µ = 0.5
Acceleration due to gravity, g = 10 m/s^2
First, we need to convert the initial speed from km/h to m/s:
Since 1 km/h = 1000/3600 m/s
u = (72 * 1000) / 3600 = 20 m/s
The frictional force acting on the car opposes its motion and is equal to the product of the coefficient of friction and the normal force. In this case, the normal force is the weight of the car, which is equal to its mass multiplied by the acceleration due to gravity:
F friction = µ * N = µ * m * g
To calculate the deceleration of the car, we need to find the frictional force. The mass of the car cancels out from both sides of the equation, so we do not need to consider it.
F friction = µ * m * g
Acceleration, a = F friction / m = (µ * m * g) / m = µ * g
Substituting the given values:
a = (0.5 * 10) m/s^2 = 5 m/s^2
Using the equation for distance with constant acceleration:
s = (u^2 - v^2) / (2 * a)
Since the car needs to be stopped, the final speed, v, is 0 m/s:
s = (u^2 - 0^2) / (2 * a) = (20^2) / (2 * 5) = 400 / 10 = 40 m
Therefore, the shortest distance in which the car can be stopped is 40 meters.
Hence, the answer is (b) 40m.