Question

A body of mass $0.5$kg travels in a straight line with velocity where a = 5 . The work done by the net force during its displacement from x = 0 to x = 2 m is.

• A. 1.5 J
• B. 50 J
• C. 10 J
• D. 100 J

Answer 1

Answer: (B)

50 J

Answer 2

Given: $\mathrm { m } = 0.5 \mathrm {~kg} , \mathrm { v } = \mathrm { kx } ^ { 3 / 2 }$

Where, $\mathrm { k } = 5 \mathrm {~m} ^ { - 1 / 2 } \mathrm {~s} ^ { - 1 }$

Acceleration,

$\left( \therefore \mathrm { v } = \frac { \mathrm { dx } } { \mathrm { dt } } \right)$

As

$\therefore$ Acceleration, $a = \frac { 3 } { 2 } k ^ { 2 } x ^ { 2 }$

Force, F = Mass × Acceleration =

Work done,

$\mathrm { w } = \frac { 3 } { 2 } \mathrm { mk } ^ { 2 } \left[ \frac { \mathrm { x } ^ { 3 } } { 3 } \right] _ { 0 } ^ { 2 } = \frac { 3 } { 6 } \times 0.5 \times 5 ^ { 2 } \times \left[ 2 ^ { 3 } - 0 \right] = 50 \mathrm {~J}$