A car is towing a trailer along a straight horizontal road by means of a horizontal tow-rope - Edexcel - A-Level Maths Mechanics - Question 6 - 2006 - Paper 1

For the trailer, the equation of motion can be written as:

$700a = T - 280$

Assuming we found $a = 0.7 \, m/s^2$ previously, we can substitute that value:

$700 \times 0.7 = T - 280$

This simplifies to:

The car continues to move with the velocity it had before the tow-rope breaks. Since it was moving at $12 \, m/s$, we can find the distance traveled in the first 4 seconds after the tow-rope breaks using:

$ext{distance} = vt + \frac{1}{2} a t^2$

Here, without any additional forces, $a = 0$, therefore:

$ext{distance} = 12 \times 4 + 0 = 48 \, m$

The assumption that the tow-rope is inextensible implies that there is no relative motion between the car and the trailer under normal circumstances. This means the acceleration of both the car and the trailer is the same while the tow-rope is intact. This simplifies calculations as we can equate the accelerations when applying equations of motion.