# mechanics question

Discussion in 'Mathematics' started by fudgesweets, Jun 4, 2011.

1. ### fudgesweetsNew commenter

A particle is moving on the x-axis. At time t=0 the particle is at the point where x=5. The velocity of the particle at time t seconds is (6t-t^2)m/s.
Find the acceleration of the particle when t=4.

I found this to be -2, so i assumed it is 2 metres per second squared deceleration, ...however the book says it is 2ms^(-2) directed towards the origin, i.e. the particle travels in the opposite direction. I am confused, surely for it to change direction the particle has to come momentarily to rest, this does not happen until t=6??

Have i missed something??

2. ### David GetlingSenior commenter

The book is correct! The acceleration is indeed directed towards the origin - which doesn't mean the velocity is.

Fudgesweets, I really hope you are a kid, because from your previous questions on this forum it is very clear that you should not be teaching A-level maths.

3. ### fudgesweetsNew commenter

yeh thanks for that, this is my moms user, i come on here to get help sometimes when she isnt around to help me out,

4. ### fudgesweetsNew commenter

i still dont understand your explanation though, if the accelaration is directed towards the origin, and the velocity is not, does this mean the particle is not travelleing towards the origin, i.e. by directed towards origin it means slowing down, deceleration?

5. ### fudgesweetsNew commenter

its ok i get it now.

6. ### David GetlingSenior commenter

I'm glad you get it. You might also like to think about motion in a circle: swinging a stone around on a string. The force that keeps the stone going round in a circle is the tension in the string, which pulls the stone towards the centre. But, since F=ma, the acceleration is also towards the centre. However, the stone certainly isn't moving towards the centre.

Hope this helps, or at least gives you something to think about.