First slide

Rectilinear Motion

Question

The velocity of a particle is v = v_o + gt + ft². If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

Moderate

A

$v_{0} - g / 2 + f$
B

$v_{0} + g / 2 + 3 f$
C

$v_{0} + g / 2 + f / 3$
D

$v_{0} + g + f$

Solution

Given, velocity $v = v_{0} + gt + {ft}^{2}$
As $v = \frac{dx}{dt}$
So, $\int_{0}^{x} dx = \int_{0}^{t} vdt = \int_{0}^{t} (v_{0} + gt + {ft}^{2}) dt$
or $v_{x} = v_{0} t + \frac{{gt}^{2}}{2} + \frac{{ft}^{3}}{3}$
When t =1, then x $= v_{0} + \frac{g}{2} + \frac{f}{3}$

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