# Dynamics 4

• September 2nd 2009, 01:10 AM
Modernized
Dynamics 4

A particle moving along a straight line experiences a retardation of 1 + v^2 cm/s^2 when it is travelling at v cm/s. If initially the velocity of the particle is u cm/s, show that it comes to rest instantaneously after Tan^-1 u s. How far has it travelled in this time?
• September 2nd 2009, 04:28 AM
mr fantastic
Quote:

Originally Posted by Modernized

A particle moving along a straight line experiences a retardation of 1 + v^2 cm/s^2 when it is travelling at v cm/s. If initially the velocity of the particle is u cm/s, show that it comes to rest instantaneously after Tan^-1 u s. How far has it travelled in this time?

$a = 1 + v^2 \Rightarrow \frac{dv}{dt} = 1 + v^2 \Rightarrow \frac{dt}{dv} = \frac{1}{1 + v^2}$.

Solve for v as a function of t, subject to the condition v = u when t = 0.

Substitute v = 0 and solve for t.

Solve $\frac{dx}{dt} = v$ for x as a function of t, subject to the condition x = 0 when t = 0. Substitute the value of t found above and solve for x.