# Speed and acceleration

## Speed and acceleration

A truck of mass 1800 kg is towing a trailer of mass 800 kg up a straight road which is
inclined to the horizontal at an angle $\inline&space;\alpha$, where $\inline&space;\sin&space;\alpha&space;=\frac{1}{20}$. The truck is connected to the trailer by a light inextensible rope which is parallel to the direction of motion of the truck. The resistances to motion of the truck and the trailer from non-gravitational forces are modelled as constant forces of magnitudes 300 N and 200 N respectively. The truck is moving at constant speed v m s–1 and the engine of the truck is working at a rate of 40 kW.

(a) Find the value of v.

As the truck is moving up the road the rope breaks.

(b) Find the acceleration of the truck immediately after the rope breaks.

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