Year 13 projectiles and variable acceleration test to download as PDF

This Year 13 projectiles and variable acceleration test lasts 40 minutes and is marked out of 20. It covers the whole chapter for pupils aged 17-18, and the full answers are on a separate page.

⏱️ Duration : 40 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Thrown from a cliff
A ball is thrown horizontally at 15 m s\(^{-1}\) from the top of a cliff 40 m above the sea.
1. Find the time to reach the sea and the horizontal distance travelled. [2 marks]
2. Find the speed and direction when it enters the sea. [2 marks]
Question 2 – Range and time of flight
A ball is projected from level ground at 26 m s\(^{-1}\) at \(35^\circ\) above the horizontal.
1. Find the time of flight. [2 marks]
2. Find the range and the greatest height. [2 marks]
Question 3 – The equation of the path
A ball is projected from the origin at 20 m s\(^{-1}\) at \(30^\circ\) above the horizontal.
1. Show that the path is \(y=x\tan30^\circ-\dfrac{gx^2}{2\times20^2\cos^230^\circ}\). [2 marks]
2. Find the height of the ball when \(x=25\) m. [2 marks]
Question 4 – Displacement and distance
A particle moves in a straight line with velocity \(v=t^2-6t+5\) m s\(^{-1}\) for \(0\le t\le5\).
1. Find when the particle is at rest. [1 mark]
2. Find its displacement from \(t=0\) to \(t=5\). [1 mark]
3. Find the total distance it travels. [2 marks]
Question 5 – Motion with position vectors
A particle has position vector \(\mathbf r=2t^2\mathbf i+(t^3-3t)\mathbf j\) metres at time \(t\) seconds.
1. Find the velocity and acceleration vectors. [2 marks]
2. Find the speed and the magnitude of the acceleration when \(t=2\). [2 marks]

How to use this Year 13 projectiles and variable acceleration test

First, revise with the projectiles and variable acceleration lesson and the worksheet. Then sit the test in one go, with a timer set to 40 minutes. After that, mark your work with the projectiles and variable acceleration test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 13 projectiles and variable acceleration test as a PDF and print it like a real exam paper. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.

Projectiles and variable acceleration – Year 13 A level maths test to download as PDF

Question 1 – Thrown from a cliff

Question 2 – Range and time of flight

Question 3 – The equation of the path

Question 4 – Displacement and distance

Question 5 – Motion with position vectors

How to use this Year 13 projectiles and variable acceleration test

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