Question

A body is moving with variable acceleration (a) along a straight line. The average acceleration of body in time interval $t_1$ to $t_2$ is

• A. $\frac{a\left[t_2+t_1\right]}{2}$
• B. $\frac{a\left[t_2-t_1\right]}{2}$
• C. $\frac{\underset{t}{\overset{t_2}{\int }}adt}{t_2+t_1}$
• D. $\frac{\underset{t_1}{\overset{t_2}{\int }}adt}{t_2-t_1}$

Answer 1

Answer: (D)

Average acceleration $=\frac{\text{ Change in velocity }}{\text{ Time }}$
$\Rightarrow a_{av}=\frac{\underset{t_1}{\overset{t_2}{\int }}adt}{t_2-t_1}$