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M2 - Differentiation on vectors

So the question is:

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A particle P moves so that at time t seconds its position vector rm relative to a fixed origin O is given by:

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

where p is a constant.

(a) Find an expression for the velocity, vm/s, at time t seconds.
(b) Given that the particle comes to instantaneous rest find the time at which it is at rest and hence the value of p.

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For part (a) I differentiated position vector r to find the velocity vector v. I got:

v = (4t-p)i+ (3t^2-3)j

But for part (b) when I try to set the velocity equal to 0, I still have unknowns t and p? How do I get rid of them?

(edited 8 years ago)

Reply 1

Dalek1099

Original post by The_Big_E

So the question is:

---

A particle P moves so that at time t seconds its position vector rm relative to a fixed origin O is given by:

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

v = (4t-p)i+ (3t^2-3)j

But for part (b) when I try to set the velocity equal to 0, I still have unknowns t and p? How do I get rid of them?

The particle comes to instantaneous rest therefore its velocity is 0i+0j m/s this means that you have two equations to solve to find p and t one of them will give you t and then you use the other to get p.