Problem

3. A van travels with constant acceleration along a straight horizontal road.

The van passes a point $A$ with speed $u\text{ m s}^{-1}$ and $20$ seconds later passes a point $B$ with speed $28\text{ m s}^{-1}$

The distance $AB$ is $400\text{ m}$.

(a) Show that $u = 12$

(b) Find the time taken for the van to travel from $A$ to the midpoint of $AB$.

The van has mass $1200\text{ kg}$.

During its motion the van experiences a constant resistive force of magnitude $260\text{ N}$

(c) Find the magnitude of the driving force exerted by the engine of the van as it travels from $A$ to $B$.