An automobile of mass is moving with speed on a straight level road

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Work Energy and Power · Work Energy and Power

Problem

An automobile of mass

m

is moving with speed

v_{0}

on a straight level road. When the driver applies the brakes, the automobile experiences a constant opposing force of magnitude

F

until it comes to rest. (i) Derive an expression for the stopping distance

s

in terms of

m

v_{0}

and

F

. (ii) From the expression obtained, show explicitly that the stopping distance is directly proportional to the square of the initial speed when the braking force remains the same. (iii) A car of mass

1200\,\text{kg}

travelling at

25\,\text{m s}^{-1}

is brought to rest by a constant braking force of

6.0\times10^{3}\,\text{N}

. Calculate the stopping distance. (iv) If the same car had been travelling at

15\,\text{m s}^{-1}

with the same braking force, what would be its stopping distance? Verify that the ratio of the two stopping distances agrees with the proportionality obtained in part (ii).

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