Turn on thread page Beta
 You are Here: Home

# m2 watch

1. A particle moves so that at time t seconds its position vector, r m , relative to a fixed origin is given by:

r = (t^2-4t)i + (t^3 - at^2)j

where a is a constant

a) find an expression for the velocity of a particle at time t seconds
b) tgiven that the particle comes to instantaneous rest, find the value of a

cant do b, any help please
2. a) v = (2t-4)i + (3t²-2at)j

b) 2t-4 = 0 => t = 2.

=> 3(2)² -2a(2) = 0 => a = 3
3. v= (2t-4)i + (3t²-2at)j

comes to rest therefore v=0,

therefore,

2t-4=0
3t²-2at=0

from the first eqn, t=2

putting t=2 in the 2nd eqn,

3*4 - 2*a*2 = 0
12 - 4a = 0
a=3
==
4. (Original post by elpaw)
a) v = (2t-4)i + (3t²-2at)j

b) 2t-4 = 0 => t = 2.

=> 3(2)² -2a(2) = 0 => a = 3
So when it comes to instantaneous rest the coeffecients of i and j(of the velocity vector) = 0 ?
5. (Original post by serious stuff)
So when it comes to instantaneous rest the coeffecients of i and j(of the velocity vector) = 0 ?
yes, thats what instantaneous rest means: the velocity is 0
6. (Original post by Fermat)
v= (2t-4)i + (3t²-2at)j

comes to rest therefore v=0,

therefore,

2t-4=0
3t²-2at=0

from the first eqn, t=2

putting t=2 in the 2nd eqn,

3*4 - 2*a*2 = 0
12 - 4a = 0
a=3
==
how do you do r = (t^2-4t)i + (t^3 - at^2) ---> v= (2t-4)i + (3t²-2at)j im very bad at vectors
7. (Original post by elpaw)
yes, thats what instantaneous rest means: the velocity is 0
Yes but does instantaneous not imply that the time it takes for the velocity to get to 0 is 0?
8. (Original post by Illuvatar)
how do you do r = (t^2-4t)i + (t^3 - at^2) ---> v= (2t-4)i + (3t²-2at)j im very bad at vectors
differentiate the components wrt t
9. (Original post by serious stuff)
Yes but does instantaneous not imply that the time it takes for the velocity to get to 0 is 0?
no, instantenaous means momentary, i.e. it will not be 0 a moment later. for example, a ball thrown up in the air is at instantaneous rest at its maximum height
10. (Original post by elpaw)
no, instantenaous means momentary, i.e. it will not be 0 a moment later. for example, a ball thrown up in the air is at instantaneous rest at its maximum height
Gotcha

Turn on thread page Beta
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: April 26, 2004
Today on TSR

### Life lessons uni will teach you

Questionable decision-making and constant surprises

### University open days

1. Loughborough University
General Open Day Undergraduate
Fri, 21 Sep '18
2. University of Cambridge
Fri, 21 Sep '18
3. Richmond, The American International University in London