Rankers Physics
Topic: Kinematics
Subtopic: Calculus Based Questions

The acceleration a of a particle starting from rest varies with time according to relation a = αt + β. The velocity of the particle after a time t will be
\[\frac{\alpha t^{2}}{2}+\beta\]
\[\frac{\alpha t^{2}}{2}+\beta t\]
\[\alpha t^{2}+\frac{1}{2}+\beta t\]
\[\frac{\left( \alpha t^{2}+\beta \right)}{2}\]

Solution:

Given acceleration:

\[
a = \alpha t + \beta
\]

The velocity after time \(t\) is:

\[
v(t) = \frac{\alpha t^2}{2} + \beta t
\]

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