Question

Consider an automobile moving at v mph that skids d feet after its brakes lock. Calculate how far it would skid if it was moving at 2v and the brakes were locked.

Answer 1

Given:

• Initial velocity is v mph.
• Displacement of skid is d feet

To find:

• Displacement of skid if initial velocity is 2v?

Calculation:

Let's assume when the brakes are locked, the surface will provide constant retardation of 'f' to the vehicle.

In 1st case, we can say:

$\therefore \: {(v2)}^{2} = {(v1)}^{2} + 2as$

$\implies \: {0}^{2} = {v}^{2} + 2( - f)d$

$\implies \: 2fd = {v}^{2}$

$\implies \: f = \dfrac{{v}^{2}}{2d} \: \: \: \: \: . \: . \: . \: . \: (1)$

Now, in 2nd case , let displacement be 's':

$\therefore \: {(v2)}^{2} = {(v1)}^{2} + 2as$

$\implies \: {0}^{2} = {(2v)}^{2} + 2( - f)s$

$\implies \: 2fs = 4 {v}^{2}$

$\implies \: s = \dfrac{2{v}^{2} }{f}$

$\implies \: s = \dfrac{2{v}^{2} }{ \frac{ {v}^{2} }{2d} }$

$\implies \: s = 4d$

So, new displacement of skid is 4d.