Consecutive motion

Here the motion is described in successive intervals of time.
In this type of problem the distance travelled is given for two successive intervals of time.
The method of solution is: Treat both sections from the starting point for the first interval, not from their individual starting points.

An example will illustrate this point

1993 Leaving Certificate Higher Level.
A particle moving in a straight line travels 30m,54m and 51m in successive intervals of 4,3,2s. Verify that the particle is moving with uniform acceleration.

Stage ab:

 

Stage ac:

Now solve two simultaneous equations in two unknowns, u and f, to give:

Stage ad: