Question

The force on a particle of mass m is given by F =26i - 12t²j where F is in N and in s. What is the magnitude of the change in the particle’s momentum between t = 1.0 s and t = 2.0 s?

Answer 1

We have,

F = 26i -12t^2j

We need to find the change in particle’s momentum between t = 1.0 s and t = 2.0 s

We know that the rate of change of momentum is equal to force.

dP/dt = 26i -12t^2j

dP = (26i -12t^2j)dt

integrating both sides we get

P = 26 t i - 4 t^3 j + constant

for t = 1

P1 = 26 x 1 i - 4 x 1^3 j + c = 26 i - 4 j + c

for t = 2

P2 = 26 x 2 i - 4 x 2^3 j + c = 52 i - 32 j + c

change in P

delta P = P2 - P1

delta P = 52 i - 32 j + c - (26 i - 4 j + c) = 26 i - 28 j

Hence, delta P = 26 i - 28 j