Question

Work done in time t on a body of mass m which is accelerated from rest to a speed v in time $t _ { 1 }$ as a function of time t is given by

• A. $\frac { 1 } { 2 } m \frac { v } { t _ { 1 } } t ^ { 2 }$
• B. $m \frac { v } { t _ { 1 } } t ^ { 2 }$
• C. $\frac { 1 } { 2 } \left( \frac { m v } { t _ { 1 } } \right) ^ { 2 } t ^ { 2 }$
• D. $\frac { 1 } { 2 } m \frac { v ^ { 2 } } { t _ { 1 } ^ { 2 } } t ^ { 2 }$

Answer 1

Answer: (D)

$\frac { 1 } { 2 } m \frac { v ^ { 2 } } { t _ { 1 } ^ { 2 } } t ^ { 2 }$

Answer 2

Work done = F.s = $m a \cdot \left( \frac { 1 } { 2 } a t ^ { 2 } \right)$ $= \frac { 1 } { 2 } m a ^ { 2 } t ^ { 2 }$

$= \frac { 1 } { 2 } m \left( \frac { v } { t _ { 1 } } \right) ^ { 2 } t ^ { 2 }$