Question

The displacement of a body varies with time as S = (t2 – 4t)m. The displacement of the body when its velocity becomes zero is?​

Answer 1

Given:

Displacement-Time relation.

$y = {t}^{2} - 4t$

To find:

Displacement when velocity becomes zero.

Calculation:

$y = {t}^{2} - 4t$

• Differentiation with respect to time will give us velocity.

$\implies \: v = \dfrac{dy}{dt}$

$\implies \: v = \dfrac{d( {t}^{2} - 4t)}{dt}$

$\implies \: v = 2t - 4$

• When velocity is zero , we can say:

$\implies \: 0= 2t - 4$

$\implies \: 2t = 4$

$\implies \: t = 0.5 \: sec$

• Now, displacement for t = 0.5 sec will be:

$\implies y = {t}^{2} - 4t$

$\implies y = {(0.5)}^{2} - 4(0.5)$

$\implies y = 0.25 - 2$

$\implies y = - 1.75 \: m$

So, net displacement is -1.75 metres.