Question

A driver of a car moving at 20m/s finds a child on tue road 50 m ahead and stops the car 10 m ahead . If mass of the car with driver is 1000 kg , calculate the force exerted by the brakes on the car and time taken to stop the car

Answer 1

Answer:

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Answer 2

The force exerted by the brakes on the car is 5000 N and time taken to stop the car is 4 seconds.

Explanation:

Given that,

Initial speed of the car, u = 20 m/s

Finally, it stops, v = 0

The child on tue road 50 m ahead and stops the car 10 m ahead. The distance covered by the car, d = 50 - 10 = 40 m

Mass of the car, m = 1000 kg

We need to find the force exerted by the brakes on the car and time taken to stop the car. It can be calculated using third equation of motion as :

$v^2-u^2=2ad$

$-u^2=2ad$

$a=\dfrac{-u^2}{2d}$

$a=\dfrac{-(20)^2}{2\times 40}$

$a=-5\ m/s^2$

Force exerted by the brakes is:

$F=ma$

$F=1000\times (-5)\ N$

F = -5000 N

Let t is the time taken by the car to stop. It is given by using first equation of motion as :

$v=u+at$

$u=-at$

$t=\dfrac{u}{-a}$

$t=\dfrac{20}{-(-5)}$

t = 4 seconds

Hence, this is the required solution.

Kinematics

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