1. 1
   A cyclist on a straight, level test track starts from rest and accelerates uniformly at 1.5 m s⁻² for 8.0 s. She then rides at constant speed for 20 s, and finally brakes with uniform deceleration, coming to rest 6.0 s after she starts braking.

   (a)

   What is the cyclist's speed at the end of the acceleration phase?

   [1 mark]

   • A6.0 m s⁻¹
   • B24 m s⁻¹
   • C12 m s⁻¹
   • D96 m s⁻¹

   (b)

   What is the total distance travelled by the cyclist?

   [1 mark]

   • A288 m
   • B324 m
   • C360 m
   • D396 m

   (c)

   Determine the cyclist's average speed for the whole journey.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   An athlete runs exactly two laps of a 400 m running track in 104 s, starting and finishing at the same point on the start line. Treat the track as a circle of circumference 400 m. Her GPS watch records her position every second.

   (a)

   What is the magnitude of the athlete's displacement at the end of the two laps?

   [1 mark]

   • A127 m
   • B400 m
   • C800 m
   • D0 m

   (b)

   Assume the athlete runs at a constant speed. What is the magnitude of her average velocity for the first 1.5 laps?

   [1 mark]

   • A1.63 m s⁻¹
   • B5.13 m s⁻¹
   • C7.69 m s⁻¹
   • D0 m s⁻¹

   (c)

   The athlete's watch reports a maximum speed of 8.9 m s⁻¹ during the race. Explain how this value can be consistent with her average speed for the two laps.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A data logger records the speed of a small electric car accelerating from rest along a straight, level road. The readings are: at t = 0 s, v = 0 m s⁻¹; at t = 2.0 s, v = 9.0 m s⁻¹; at t = 4.0 s, v = 15.0 m s⁻¹; at t = 6.0 s, v = 19.0 m s⁻¹; at t = 8.0 s, v = 21.0 m s⁻¹. The speed increases smoothly between readings.

   (a)

   Deduce, using the data, whether the car's acceleration is uniform, and estimate the car's instantaneous acceleration at t = 4.0 s.

   [3 marks]

   (b)

   A student calculates the distance travelled in the first 8.0 s using s = ((u + v)/2)t and obtains 84 m. Evaluate the student's method and determine a better estimate of the distance travelled.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A football is kicked from ground level on a flat pitch with a speed of 18.0 m s⁻¹ at an angle of 35° above the horizontal, directly towards a goal. The goal line is 28.0 m from the kicking point and the crossbar of the goal is 2.44 m above the ground. Take g = 9.81 m s⁻².

   (a)

   Ignoring air resistance, determine the time of flight and range of the ball if it is not obstructed, and deduce whether it passes below the crossbar when it reaches the goal line.

   [6 marks]

   (b)

   In reality air resistance acts on the ball. Discuss how air resistance affects the ball's trajectory, time of flight, range, velocity and acceleration, and whether your conclusion about the crossbar remains reliable. Explain also why a ball dropped from a very tall building eventually stops accelerating.

   [6 marks]

   Total for question 4: 12 marks

End of questions