The diagram shows the velocity-time graph of a particle P moving in a straight line with velocity v ms⁻¹ at time t s after leaving a fixed point. [Figure P shows a velocity-time graph] Find the distance travelled by the particle P.

1. (a)The diagram shows the velocity-time graph of a particle P moving in a straight line with velocity v ms⁻¹ at time t s after leaving a fixed point. [Figure P shows a velocity-time graph] Find the distance travelled by the particle P.[2]
2. (b)The diagram shows the displacement-time graph of a particle Q moving in a straight line with displacement s m from a fixed point at time t s. [Figure Q shows a displacement-time graph] On the axes below, plot the corresponding velocity-time graph for the particle Q.[3]
3. (c)The displacement s m of a particle R, which is moving in a straight line, from a fixed point at time t s is given by s = 4t - 16ln(t+1) + 13.
4. (c)(i)Find the value of t for which the particle R is instantaneously at rest.[3]
5. (c)(ii)Find the value of t for which the acceleration of the particle R is 0.25ms⁻².[2]

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