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” …