1) Which of the following pairs contains one vector and one scalar quantity? [1]
A: displacement : mass
B: displacement : velocity
C: distance : speed
D: speed : time

2) A vector P of magnitude $3.0 N$ acts towards the right and a vector Q of magnitude $4.0 N$ acts upwards. [1]
What is the magnitude and direction of the vector (P − Q)?
A: $1.0 N$ at an angle of ${53^ \circ }$ downwards to the direction of P
B: $1.0 N$ at an angle of ${53^ \circ }$ upwards to the direction of P
C: $5.0 N$ at an angle of ${53^ \circ }$ downwards to the direction of P
D: $5.0 N$ at an angle of ${53^ \circ }$ upwards to the direction of P

3) A car travels one complete lap around a circular track at a constant speed of $120\,km\,{h^{ - 1}}$.
a: If one lap takes 2.0 minutes, show that the length of the track is $4.0 km$. [2]
b: Explain why values for the average speed and average velocity are different. [1]
c: Determine the magnitude of the displacement of the car in a time of $1.0 min$. [2]
(The circumference of a $circle = 2\pi r$, where R is the radius of the circle.) [Total: 5]

4) A boat leaves point A and travels in a straight line to point B. The journey takes $60 s$.

Calculate:
a: the distance travelled by the boat [2]
b: the total displacement of the boat [2]
c: the average velocity of the boat. [2]
Remember that each vector quantity must be given a direction as well as a magnitude. [Total: 6]

5) A boat travels at $2.0\,m\,{s^{ - 1}}$ east towards a port, $2.2 km$ away. When the boat reaches the port, the passengers travel in a car due north for 15 minutes at $60\,k\,{m^{ - 1}}$
Calculate:
a: the total distance travelled [2]
b: the total displacement [3]
c: the total time taken [2]
d: the average speed in $m\,{s^{ - 1}}$ [2]
e: the magnitude of the average velocity. [2]
[Total: 11]

6) A river flows from west to east with a constant velocity of $1.0\,m\,{s^{ - 1}}$. A boat leaves the south bank heading due north at $12.4\,m\,{s^{ - 1}}$. Find the resultant velocity of the boat. [3]

7) a: Define displacement. [1]
b: Use the definition of displacement to explain how it is possible for an athlete to run round a track yet have no displacement. [2]
[Total: 6]

8) A girl is riding a bicycle at a constant velocity of $3.0\,m\,{s^{ - 1}}$ along a straight road. At time $t = 0$, she passes her brother sitting on a stationary bicycle. At time $t = 0$, the boy sets off to catch up with his sister. His velocity increases from time $t = 0$ until $t = 5.0s$, when he has covered a distance of $10 m$. He then continues at a constant velocity of $4.0\,m\,{s^{ - 1}}$.
a: Draw the displacement–time graph for the girl from $t = 0$ to $t = 12s$. [1]
b: On the same graph axes, draw the displacement–time graph for the boy. [2]
c: Using your graph, determine the value of t when the boy catches up with his sister. [1]
[Total: 4]

9) A student drops a small black sphere alongside a vertical scale marked in centimetres. A number of flash photographs of the sphere are taken at $0.10 s$ 
intervals:

The first photograph is taken with the sphere at the top at time $t = 0 s$.
a: Explain how Figure 1.19 shows that the sphere reaches a constant speed. [2]
b: Determine the constant speed reached by the sphere. [2]
c: Determine the distance that the sphere has fallen when $t = 0.80 s$. [2]
d: In a real photograph, each image of the sphere appears slightly blurred because each flash is not instantaneous and takes a time of $0.0010 s$.
Determine the absolute uncertainty that this gives in the position of each position of the black sphere when it is travelling at the final constant speed.
Suggest whether this should be observable on the diagram. [2]
[Total: 8]

10) a: State one difference between a scalar quantity and a vector quantity and give an example of each. [3]
b: A plane has an air speed of $500k\,m\,{h^{ - 1}}$ due north. A wind blows at $100k\,m\,{h^{ - 1}}$ from east to west.
Draw a vector diagram to calculate the resultant velocity of the plane. Give the direction of travel of the plane with respect to north. [4]
c: The plane flies for 15 minutes. Calculate the displacement of the plane in this time. [1]
[Total: 8]

11) A small aircraft for one person is used on a short horizontal flight. On its journey from A to B, the resultant velocity of the aircraft is $15\,m\,{s^{ - 1}}$ in a direction ${60^ \circ }$ east of north and the wind velocity is $7.5\,m\,{s^{ - 1}}$ due north.

a: Show that for the aircraft to travel from A to B it should be pointed due east. [2]
b: After flying $5 km$ from A to B, the aircraft returns along the same path from B to A with a resultant velocity of $13.5\,m\,{s^{ - 1}}$. Assuming that the time spent at B is negligible, calculate the average speed for the complete journey from A to B and back to A.