A toy train moves on a straight track

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A toy train moves on a straight track. Let its initial position (point

A

) be

x_0

metres. It then undergoes three successive displacements:

+d

metres,

-2d

metres and

+\dfrac{d}{2}

metres. (i) Write the coordinate of the train after each displacement in terms of

x_0

and

d

. (ii) Derive a simplified expression for the final coordinate

x_f

after all three displacements. (iii) The train is now brought back to point

A

by a single displacement. Derive the magnitude and direction of this displacement in terms of

d

. (iv) For

d = 60\,\text{m}

and

x_0 = -40\,\text{m}

, calculate all coordinates obtained in part (i), the value of

x_f

from part (ii) and the displacement found in part (iii).