Question

*For uniformly accelerated motion, the velocity attained by a particle after time 't' will be:*​

Answer 1

Given:

An object is uniformly accelerated.

To find:

Velocity attained after time t ?

Calculation:

Since, acceleration is said to be constant, we can apply the 1st Law of Kinematics as follows:

$\boxed{ \bf \: v = u + at}$

'v' is final Velocity, 'u' is initial velocity.

This can be also proved with calculus:

Let acceleration be constant and equal to 'a'.

$\therefore \: acc. = a$

$\implies \: \dfrac{dv}{dt} = a$

$\implies \: dv = a \: dt$

Integrating on both sides:

$\displaystyle\implies \:\int_{u}^{v} dv = a \int_{0}^{t}\: dt$

$\displaystyle\implies \:v - u = a(t - 0)$

$\displaystyle\implies \:v - u = at$

$\displaystyle\implies \:v = u + at$

[Hence Proved]