Question

A Car is moving with a non-uniform velocity towards East. [05 Marks] Its velocity changes at different time intervals. Calculate the instantaneous velocity at time 3 sec. The distance is given by equation 2t2 – 4t

Answer 1

Given:

A Car is moving with a non-uniform velocity towards East. [05 Marks] Its velocity changes at different time intervals. The distance is given by equation 2t² – 4t.

To find:

Instantaneous velocity at t = 3 sec.

Calculation:

The instantaneous velocity of an object can be easily calculated from the 1st order derivative of the displacement (time) function with respect to time.

$\rm \therefore \: x = 2 {t}^{2} - 4t$

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

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

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

$\rm \implies \: v = 2(2t) - 4(1)$

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

$\rm \implies \: v \bigg|_{t = 3 \: sec} = 4(3) - 4$

$\rm \implies \: v \bigg|_{t = 3 \: sec} = 12 - 4$

$\rm \implies \: v \bigg|_{t = 3 \: sec} = 8 \: m {s}^{ - 1}$

So, instantaneous velocity at t = 3 sec is 8 m/s.