Three velocity vectors, u, v and X are shown in the diagram.
Which statement about the vectors is correct? A B C D 6
v added to u produces a resultant X u added to X produces a resultant v the magnitude of v equals the sum of the magnitude of u and the magnitude of X the magnitude of u equals the sum of the magnitude of X and the magnitude of v.
Explain what is meant by: a a scalar quantity b a vector quantity.
Name any three scalar quantities.
a Define the velocity of an object. b Use your answer to a to explain why velocity is a vector quantity.
Cannons are being fired in a mock battle scene. The spectators are at a safe distance of 600 m from the cannons. Calculate how long it would take for the sound from the cannons to reach the spectators. (Speed of sound in air = 340 m s−1.)
10 A small insect travels a distance of 24 cm in a time of 4.0 minutes. Calculate the average speed of the insect in m s−1.
11 The displacement–time graph for an object is shown below.
a What does the gradient of a displacement–time graph represent? b Describe the journey of the object. c Calculate the velocity of the object at 2.0 s.
  
12 A cyclist travels a distance of 3.2 km in 15 minutes. She rests for 30 minutes. She then covers a further distance of 6.2 km in a time of 40 minutes. Calculate the average speed of the cyclist in m s−1: a for the first 15 minutes of the journey b for the total journey.
13 The diagram shows the displacement–time graph for an object.
Calculate the velocity of the object at times: a 4.0 s b 8.0 s.
14 The diagram below shows a stone moving in a horizontal circle of radius 70 cm.
The stone takes a time of 0.62 s for each revolution. a
Calculate the speed of the stone. (Hint: In a time of 0.62 s, the stone travels a distance equal to the circumference of the circle.) b The stone starts at point A. What is the magnitude of the displacement of the stone from A after a time of: i 0.31 s ii 0.62 s?
15 The table below shows the time taken (t) and the displacement (s) of a trolley rolling down a ramp. Time / s
Displacement / 10−2 m
a Plot a graph of displacement against time. (Make sure that you sketch a smooth curve.) b Describe the motion of the trolley. Explain your answer. c By drawing tangents to the curve at times 0.2 s and 0.5 s, determine the velocities of the trolley at these times. d The acceleration a of the trolley is given by:
  
change in velocity time taken
Use the equation above and your answers to c to determine the acceleration a of the trolley.  Total: