The initial velocity of a particle is u (at t=0) and the accelerati

Discussion Forum : Motion In One Dimension

Question -

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

Options:

A .

v = u + a t^{2}

B .

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

C .

v = u + a t

D . v = u

Answer: Option B
:
B

We have $f = \frac{d v}{d t}$

On rearrangement and integration

$\int_{u}^{v} d v = a \int_{0}^{t} t d t$

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

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

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