Question

The relation, x = t-t2 describes the position of a particle in one direction with respect to time where x Is in meters and t is in second. the position, x when velocity is zero, is :
1m,-1/2m,3/4m Or -1/4 m???​

Answer 1

Given:

x = t - t² is the relation between displacement and time.

To find:

Position when velocity is zero?

Calculation:

$x = t - {t}^{2}$

• Differentiation w.r.t time:

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

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

$\implies \: v = 1 - 2t$

• For velocity being zero, we can say:

$\implies \: 0 = 1 - 2t$

$\implies \: 2t = 1$

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

• Now, putting value of t in first equation:

$\implies x = t - {t}^{2}$

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

$\implies x = 0.5 - 0.25$

$\implies x = 0.25 \: m$

$\implies x = \dfrac{1}{4} \: m$

So, position when velocity is zero is ¼ metres.