Not all suvat questions can be solved with a single application of the suvat formulae. Sometimes two applications are required, simultaneous equations are formed and these must be solved.

A particle starts from rest at a point O. It accelerates uniformly to a pint Pin 2 seconds, at which it has speed u. It continues to accelerate with the same constant acceleration to a point Q in a further 3 seconds. at which it has speed v. PQ=5m. Find the speed at P, the speed at Q and the distance PQ.

A diagram is drawn.

The acceleration is constant. Call it k. The final speed at P for the motion OP equals the initial speed at P for the motion PQ. Call it c.

Apply suvat to the motion OP.

s=

u=0

v=c

a=k

t=t

Application of the equationgives (1)

Apply suvat to the motion PQ.

s=5

u=c

v=

a=k

t=4

Use the equationto give

Sub (1) into (2) to give

Then from (1)