An object has a velocity $u$ at time $t = 0$ , it is undergoing retardation $a$ and covers a distance $s$ attaining a velocity $v$ in time $t$ . Which of the following equations of motion correctly describe the motion?

$u = v - a t$

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$s = u t + \frac{1}{2} a t^{2}$

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$u^{2} = 2 a s + v^{2}$

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$u = v + a t$

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Solution

The correct options are
C
$u^{2} = 2 a s + v^{2}$

D
$u = v + a t$

Equations of motion of a body accelerating uniformly are:

$A$ is the acceleration of the body

1. $v = u + A t$

2. $s = u t + \frac{1}{2} A t^{2}$

3. $v^{2} = u^{2} + 2 A s$

Given, the deceleration of the body = $a$

So, the acceleration of the body is $- a$

Substituting, $A = - a$ in equations 1, 2 and 3 we get:

$v = u - a t ⟹ u = v + a t$

$s = u t - \frac{1}{2} a t^{2}$

$v^{2} = u^{2} - 2 a s ⟹ u^{2} = v^{2} + 2 a s$

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An object has a velocity u at time t=0, it is undergoing retardation a and covers a distance s attaining a velocity v in time t. Which of the following equations of motion correctly describe the motion?

An object has a velocity $u$ at time $t = 0$ , it is undergoing retardation $a$ and covers a distance $s$ attaining a velocity $v$ in time $t$ . Which of the following equations of motion correctly describe the motion?