Question

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

A
v=u+at2
B
v=u+at22
C
v=u+at
D
v=u

Solution

## The correct option is B $$\displaystyle v=u+\frac{at^{2}}{2}$$As $$\displaystyle f=at\;\;\;\;\Rightarrow \dfrac{dv}{dt}=at$$$$\displaystyle \Rightarrow \int_{u}^{v}dv=\int_{0}^{t}at\;\;dt\;\;\Rightarrow v-u=\dfrac{at^{2}}{2}$$$$\displaystyle \Rightarrow v=u+\dfrac{1}{2}at^{2}$$Physics

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