Question

A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by $x = 3 t - 4 t ^ { 2 } + t ^ { 3 }$, where x is in metres and t is in seconds. The work done during the first 4 seconds is

• A. 5.28 J
• B. 450 Mj
• C. 490 mJ
• D. 530 mJ

Answer 1

Answer: (A)

5.28 J

Answer 2

$v = \frac { d x } { d t } = 3 - 8 t + 3 t ^ { 2 }$

∴ $v _ { 0 } = 3 \mathrm {~m} / \mathrm { s }$ and $v _ { 4 } = 19 \mathrm {~m} / \mathrm { s }$

$W = \frac { 1 } { 2 } m \left( v _ { 4 } ^ { 2 } - v _ { 0 } ^ { 2 } \right)$ (According to work energy theorem)