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>>Physics
>>Motion in a Straight Line
>>Acceleration
>> $The initial velocity of a particle is u$

Question

The initial velocity of a particle is $u$ $(a t t = 0)$ and the acceleration is given by $f = a t$ . Which of the following relations is valid?

A

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

B

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

C

$v = u + a t$

D

$v = u$

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Solution

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Correct option is B)

As $f = a t \Rightarrow \frac{d v}{d t} = a t$

$\Rightarrow \int_{u}^{v} d v = \int_{0}^{t} a t d t \Rightarrow v - u = \frac{a t ^{2}}{2}$

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

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