First slide

Newton's laws of motion

Question

A car moving at a speed v is stopped by a retarding force F in a distance s. If the speed of the car was 3v, the force needed to stop it within the same distance s will be

Moderate

A

3 F
B

6 F
C

9 F
D

12 F

Solution

Let m be the mass of the car and a be the deceleration produced by force F, then F= ma, where a is given by $2 as = v^{2} or a = \frac{v^{2}}{2 s}$ .
Therefore, $F = \frac{{mv}^{2}}{2 s} .$
$Thus F \propto v^{2}$ .
If v is increased by 3 times, F will increase by 9 times.

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