Question

A body of mass 3 kg is under a force, which causes a displacement in it is given by $S = \frac { t ^ { 3 } } { 3 }$ (in m). Find the work done by the force in first 2 seconds

• A. 2 J
• B. 3.8 J
• C. 5.2 J
• D. 24 J

Answer 1

Answer: (D)

24 J

Answer 2

$S = \frac { t ^ { 3 } } { 3 }$∴ $d S = t ^ { 2 } d t$

Now work done by the force

$\int _ { 0 } ^ { 2 } 3 \times 2 t \times t ^ { 2 } d t$ $= \int _ { 0 } ^ { 2 } 6 t ^ { 3 } d t$= = 24 J