Mathematics 9709 · AS & A Level · Momentum

Momentum — practice question

On a straight horizontal test track, driverless vehicles, with no passengers, are undergoing testing. A car of mass $1600\ \text{kg}$ is pulling a trailer of mass $700\ \text{kg}$ along the track. The brakes are applied, producing a deceleration of $12\ \text{m\ s}^{-2}$. The braking force acts only on the car. In addition to the braking force, there are constant resistance forces of $600\ \text{N}$ on the car and $200\ \text{N}$ on the trailer.
(a)[2]

Determine the magnitude of the force in the tow-bar.

(b)[2]

Determine the braking force.

(c)[2]

When the brakes are first applied, the car is travelling at $22\,\text{m s}^{-1}$. At that moment the car is $17.5\,\text{m}$ from a van at rest, directly ahead of it. Show that the car collides with the van at a speed of $8\,\text{m s}^{-1}$.

(d)[3]

After the collision, the van moves off at $5\,\text{m s}^{-1}$ and the car together with the trailer keeps moving in the same direction at $2\,\text{m s}^{-1}$. Determine the mass of the van.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Newton’s second law applied to the car, trailer or entire system, with $F$ eliminated

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