9709/41/M/J/25q7

A particle X moves along a straight track, starting from a point O at time t=0. The displacement of X from O at time t s is s m, where .

(a) Find the time at which X is instantaneously at rest, and hence find the total distance travelled by X between t=0 and t=16. [6 marks]

A second particle Y moves along another straight track, starting from a point P at time t=0. The acceleration of Y at time t is a ms^-2, where a = 0.8 – 0.6t. The velocity of Y when it leaves P is 7.5ms^-1.

(b) When the velocity of Y is -9.6ms^-1, show that the displacement of X from O is equal to the displacement of Y from P. [7 marks]

9709/42/M/J/25q6

A particle P moves in a straight line and passes through the point A at time t=0. The velocity v ms^-1 of P at time t seconds is given by v = (2t+1)^3/2 – 2t², where

(a) Find the maximum velocity of P in the interval [5 marks]

It is given that in the interval the velocity of P is always positive.

(b) Find the distance of P from A at the instant when P is moving at this maximum velocity. [4 marks]

9709/43/M/J/25q7

A particle X moves in a straight line. The displacement of X from O at time t s after leaving O is s m, where s = 0.35t² + 0.6t for .

(a) Find the velocity of X at t = 4. [2 marks]

For t > 4, the acceleration of X at time t s after leaving O is a ms^-2, where a = 0.3t^1/2. There is no change in the velocity of X at t=4. The velocity of X at t = T is 14.2ms^-1.

(b) (i) Find the value of T. [4 marks]

(ii) Find the total distance travelled by X between t=0 and t=T. [4 marks]

9709/41/O/N/24q8

A particle P moves in a straight line, passing through a point O with velocity 4.2ms^-1. At time t s after P passes O, the acceleration, a ms^-2, of P is given by a = 0.6t – 2.7.

Find the distance P travels between the times at which it is at instantaneous rest. [7 marks]