A motor car running at the rate of 7ms−1 can be stopped by its brakes in 10 m. Prove that the total resistance to the motion, when the brakes are on, is one fourth of the weight of the car.
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Solution
Initial velocity, u=7m/s
Distance traveled, s=10m
Final velocity, v=0m/s
According to equation of motion we know that,
v2−u2=2as
To determine acceleration consider the force acting on the car when breaks were applied that is
F=μmg
which will cause deceleration of the car ∴a=−μg by comparing F=μmg and F=ma
Substitute in equation of motion above,
v2−u2=2as=−2μgs
u2=2μgs
μ=u22gs=492×9.8×10=14
Therefore, force acting on the car when breaks were applied that is