Question

A car is stopped in a distance D by a constant friction force that is independent of the car's speed. A)What is the stopping distance (in terms of D) if the speed is the same as it originally was but the friction force is tripled? (Solve using the work-energy theorem.) S=?D

Answer 1

from work energy theorem,

W_friction = KE

or, -fD = KE_f - KE_i

or, -fD = 0 - KE_i

or, fD = KE_i

now, friction force is tripled. Let the distance travelled be d. Also, KE_i remains the same since speed is same.

so, W_friction = KE

or, -(3f)d = KE_f - KE_i

or, -3fd = 0 - KE_i

or, 3fd = KE_i

but KE_i = fD

so, 3fd = fD

or, d = D/3 is stopping distance

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