Question

A motorcycle of mass m resting on a frictionless road moves under the influence of a constant force F. The work done by this force in moving the motorcycle is given by F²t²/2m, where t is the time in seconds.

Ratio of instantaneous power to average power of the motorcycle in t = T second is

• A. 1 : 1
• B. 2 : 1
• C. 3 : 2
• D. 1 : 2

Answer 1

Answer: (B)

2 : 1

Answer 2

For instantaneous power

dP = $\frac { \mathrm { dW } } { \mathrm { dt } } = \frac { \mathrm { dF } ^ { 2 } \mathrm { t } ^ { 2 } } { 2 \mathrm {~m} } = \frac { \mathrm { F } ^ { 2 } } { 2 \mathrm {~m} } \cdot 2 \mathrm { t }$

or dP= $\frac { 2 \mathrm {~F} ^ { 2 } \mathrm {~T} } { 2 \mathrm {~m} }$

But average power =

∴ Instantaneous power : average power = 2 : 1.