The Student Room Group

Dynamics Problem

Hey, does anyone have any idea how to solve this? Completely lost... :frown:

A particle of unit mass moves along the x-axis under the influence of a resistive force βˆ’kv^n i, where k is a positive constant and v is the magnitude of the velocity v at time t.
Find the times and distances at which the particle comes to rest, i.e. v = 0, for the following cases:

(i) n < 1,
(ii) 1 < n < 2,

You may assume that at t = 0, x = 0 and v = v0
Reply 1
Have you tried F=ma?
Reply 2
Original post by msmith2512
Have you tried F=ma?


Yeah, I put F = ma = -kv^n as the equation of motion. Not really sure where to go next?

I tried getting an expression for t (by solving as a differential equation) but then how do I use the two different conditions? (n<1 and 1<n<2)
Reply 3
Original post by ltully10
Yeah, I put F = ma = -kv^n as the equation of motion. Not really sure where to go next?

I tried getting an expression for t (by solving as a differential equation) but then how do I use the two different conditions? (n<1 and 1<n<2)


You will have to look at each case separately so firstly solve completely for n=1. Then solve completely from scratch for 1<n<2.

You may also need the identity that a=dv/dt = (dv/dx).(dx/dt) = v dv/dx - not sure if you have seen this before but it is well worth knowing. x = displacement from origin (i.e. position).

Quick Reply