Edexcel AS Paper 2 (AS Paper 2) 2024 June

1. \begin{figure}[h] \end{figure} Figure 1 shows the speed-time graph for the journey of a car moving in a long queue of traffic on a straight horizontal road. At time \(\mathrm { t } = 0\), the car is at rest at the point A .
The car then accelerates uniformly for 5 seconds until it reaches a speed of \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
For the next 15 seconds the car travels at a constant speed of \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
The car then decelerates uniformly until it comes to rest at the point B.
The total journey time is 30 seconds.

1. Find the distance AB .
2. Sketch a distance-time graph for the journey of the car from A to B .

1. In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.

A particle is moving along a straight line.
At time t seconds, \(\mathrm { t } > 0\), the velocity of the particle is \(\mathrm { Vms } ^ { - 1 }\), where $$v = 2 t - 7 \sqrt { t } + 6$$

1. Find the acceleration of the particle when \(t = 4\) When \(\mathrm { t } = 1\) the particle is at the point X .
   When \(\mathrm { t } = 2\) the particle is at the point Y . Given that the particle does not come to instantaneous rest in the interval \(1 < \mathrm { t } < 2\)
2. show that \(X Y = \frac { 1 } { 3 } ( 41 - 28 \sqrt { 2 } )\) metres.

1. \hspace{0pt} [In this question, \(\mathbf { i }\) and \(\mathbf { j }\) are perpendi cular unit vectors in a horizontal plane]

A particle P is moving on a smooth horizontal surface under the action of two forces.
Given that

• the mass of P is 2 kg
• the two forces are \(( 2 \mathbf { i } + 4 \mathbf { j } ) \mathrm { N }\) and \(( \mathbf { i } - 2 \mathbf { j } ) \mathrm { N }\), where C is a constant
• the magnitude of the acceleration of P is \(\sqrt { 5 } \mathrm {~m} \mathrm {~s} ^ { - 2 }\)
  find the two possible values of C .

4. \begin{figure}[h] \end{figure} Figure 2 shows a car towing a trailer along a straight horizontal road.
The mass of the car is 800 kg and the mass of the trailer is 600 kg .
The trailer is attached to the car by a towbar which is parallel to the road and parallel to the direction of motion of the car and the trailer. The towbar is modelled as a light rod.
The resistance to the motion of the car is modelled as a constant force of magnitude 400 N .
The resistance to the motion of the trailer is modelled as a constant force of magnitude R newtons. The engine of the car is producing a constant driving force that is horizontal and of magnitude 1740 N. The acceleration of the car is \(0.6 \mathrm {~ms} ^ { - 2 }\) and the tension in the towbar is T newtons.
Using the model,

1. show that \(\mathrm { R } = 500\)
2. find the value of T . At the instant when the speed of the car and the trailer is \(12.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the towbar breaks.
   The trailer moves a further distance d metres before coming to rest.
   The resistance to the motion of the trailer is modelled as a constant force of magnitude 500 N. Using the model,
3. show that, after the towbar breaks, the deceleration of the trailer is \(\frac { 5 } { 6 } \mathrm {~ms} ^ { - 2 }\)
4. find the value of d. In reality, the distance d metres is likely to be different from the answer found in part (d).
5. Give two different reasons why this is the case.