# Distances and velocities

• Mar 17th 2009, 11:11 AM
gracey
Distances and velocities
A particle starts from rest at O and travels to A. The journey from O to A takes 25 seconds. The particle reaches A with a speed of 15ms. the velocity of the particle t seconds after it leaves 0 is vms. It is given that v=kt²

Find the distance O to A

Find the distance of the particle from 0 when its acceleration is 0.72m/s/s

thanks for any help (Nod)
• Mar 17th 2009, 01:23 PM
Distance and velocity
Hello gracey
Quote:

Originally Posted by gracey
A particle starts from rest at O and travels to A. The journey from O to A takes 25 seconds. The particle reaches A with a speed of 15ms. the velocity of the particle t seconds after it leaves 0 is vms. It is given that v=kt

Quote:

Originally Posted by gracey
²

Find the distance O to A

Find the distance of the particle from 0 when its acceleration is 0.72m/s/s

thanks for any help (Nod)

First, find the value of $k$ using the fact that when $t = 25, v = 15$.

Then, writing the velocity as $\frac{ds}{dt}$ (where $s$ is the distance of the particle from O), solve the equation $\frac{ds}{dt}= kt^2$ by integration, using your value of $k$.

You know that when $t = 0, s = 0$; and you need the value of $s$ when $t = 25$.

For the last part, the acceleration is $a = \frac{dv}{dt}$. So if you differentiate $v = kt^2$, you'll get a formula for $a$ in terms of $t$. Use this to find $t$ when $a = 0.72$; then plug this value of $t$ into your equation for $s$ to find the distance from O.

Can you complete it now?