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. $\frac{\int\limits_{t}^{t_{2}} a d t}{t_{2}+t_{1}}$
• D. $\frac{\int\limits_{t_{1}}^{t_{2}} a d t}{t_{2}-t_{1}}$

Answer 1

Answer: (D)

Average acceleration $=\frac{\text { Change in velocity }}{\text { Time }}$
$\Rightarrow a_{ av }=\frac{\int\limits_{t_{1}}^{t_{2}} a\, d t}{t_{2}-t_{1}}$