Question

A force F = kt(τ - t) acts on a particle of mass m, which is at rest at t = 0 where k is a constant. Find the momentum of the force when the action of the force is discontinued.

• A. $\frac { \mathrm { k } \tau ^ { 3 } } { 2 }$
• B.
• C.
• D.

Answer 1

Answer: (C)

Answer 2

∆p = $\int \mathrm { Fdt } = \int _ { 0 } ^ { \tau } \mathrm { kt } ( \tau - \mathrm { t } ) \mathrm { dt } = \frac { \mathrm { k } \tau ^ { 3 } } { 2 } - \frac { \mathrm { k } \tau ^ { 3 } } { 3 } = \frac { \mathrm { k } \tau ^ { 4 } } { 6 }$.