1. ## 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

2. ## Distance and velocity

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

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

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

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

Can you complete it now?