Vertical motion with resistance force

A question is this type if and only if a particle moves vertically under gravity with an additional constant resistance force and you must find acceleration, speed, or distance.

3 questions · Standard +0.1

3.02d Constant acceleration: SUVAT formulae
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Edexcel M1 2023 June Q3
8 marks Standard +0.3
  1. Two students observe a book of mass 0.2 kg fall vertically from rest from a shelf that is 1.5 m above the floor.
Student \(A\) suggests that the book is modelled as a particle falling freely under gravity.
  1. Use student \(A\) 's model to find the time taken for the book to reach the floor. Student \(B\) suggests an improved model where the book is modelled as a particle experiencing a constant resistance to motion of magnitude \(R\) newtons. Given that the time taken for the book to reach the floor is 0.6 seconds,
  2. use student \(B\) 's model to find the value of \(R\)
Edexcel M1 2024 June Q5
14 marks Standard +0.3
  1. A parachute is used to deliver a box of supplies. The parachute is attached to the box.
  • the parachute and box are dropped from rest from a helicopter that is hovering at a height of 520 m above the ground
  • the parachute and box fall vertically and freely under gravity for 5 seconds, then the parachute opens
  • from the instant the parachute opens, it provides a resistance to motion of magnitude 3200 N
  • the parachute and box continue to fall vertically downwards after the parachute opens
  • the parachute and box are modelled throughout the motion as a particle \(P\) of mass 250 kg
    1. Find the distance fallen by \(P\) in the first 5 seconds.
    2. Find the speed with which \(P\) lands on the ground.
    3. Find the total time from the instant when \(P\) is dropped from the helicopter to the instant when \(P\) lands on the ground.
    4. Sketch a speed-time graph for the motion of \(P\) from the instant when \(P\) is dropped from the helicopter to the instant when \(P\) lands on the ground.
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AQA M1 2010 January Q4
10 marks Moderate -0.3
4 A ball is released from rest at a height of 15 metres above ground level.
  1. Find the speed of the ball when it hits the ground, assuming that no air resistance acts on the ball.
  2. In fact, air resistance does act on the ball. Assume that the air resistance force has a constant magnitude of 0.9 newtons. The ball has a mass of 0.5 kg .
    1. Draw a diagram to show the forces acting on the ball, including the magnitudes of the forces acting.
    2. Show that the acceleration of the ball is \(8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
    3. Find the speed at which the ball hits the ground.
    4. Explain why the assumption that the air resistance force is constant may not be valid.