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**helloying** 1)A particle move in a straight line so that its distance, s metres, from a fixed point is given by s=t^3(2-t)^2, where t is the time in seconds aftre passing through the fixed point.

Find (i) the values of t when the particle is at rest

(ii)the greatest distance travelled by the particle.

For 1)(i)i think the velocity is 0 when the paricle is at rest. So i ds/dt=0

However i could not get the values right. my ds/dt is 12t^2-32t^3+5t^4. I checked the ans but it is wrong. can anyone help me please? Mr F says: Please show the details of how you got your answer. Using the product rule, I get ds/dt = t^2 (2 - t) (6 - 4t).

For1)(ii)i think the greatest distance travelled is when velocity is at =0 Is it correct? Mr F says: There is no finite answer if the question is as you've worded it.

Another question:A particle P starts from point A and moves in a straight line so that its displacement s in metres, from a fixed point O, t seconds after leaving A is given by s=5+t(t-5)^2

Find the total distance travelled from t=0 to t=5.