kinematics vector and scalar definitions scalar: a physical quantity that can be defined by...

Kinematics

Vector and Scalar Definitions

Scalar: a physical quantity that can be defined by

magnitude (size) only.

Vector: a physical quantity that can be defined by

magnitude and direction.

Scalar examples: distance, time, mass, speed, energy.

Vector examples: displacement, acceleration, velocity, force, momentum.

NOTES p.1

Distance and Displacement

A walker takes the following path (green line).N

S

EWThe total distance walked is shown in green.

The total displacementis shown in red as a straightline from start to finish with magnitude, x, in direction, East of North.

Start

Finish

N x

Calculating Speed and Velocity

• These are two different quantities. Remember, speed is a scalar and velocity is a vector.

speed = distance time

velocity = displacement time

NOTE – to find the direction of the velocityuse the direction of the displacement.

NOTES p.2

TRY THIS IN PAIRS

Find the distance travelled, the overall displacement, the average speed and the average velocity for a person who walks 5km, North followed by 3km, South in a time of 2 hours.

3km5km

TRY THIS IN PAIRS

Find the distance travelled, the overall displacement, the average speed and the average velocity for a person who walks 5km, North followed by 5km, East followed by 7km, South in a time of 6 hours.

7km

5km

5km

A car moves 30m North, then 50m West, then 30m South in 1 minute.

a) What’s the speed of the car?b) What’s the velocity of the car?

Example 1

NOTES p. 2

a) Speed = dist / t = 110 / 60 = 1.83 ms-1

3 cm = 30m

5cm = 50m

3cm = 30m

5cm = 50m

Distance = 30 + 50 + 30 = 110m

Displacement = 50m, West

b) Velocity = disp / t = (50, West) / 60

= 0.83 ms-1, West

1cm = 10mN

Example 2

Use a scale diagram to calculate the displacement of a man who walks 40m, North then 100m at 120o.

4 cm = 40m

10cm = 100m

120o

x

x = cm = m. = o.

Displacement = m at o.87 097

Example 3

Use Pythagoras and trigonometry to calculate the displacement of a man who walks 40m, North then 50m, East then 10m, South.

10m

50m

40m

x

50m

40 – 10 = 30m x

resultant displacement magnitude (x): x2 = 302

+ 502

= 3400

x = 58.3mdirection : tan = opp = 50 adj 30

= 59o (= 059 o from North)

SO…displacement = 58 m at a bearing of 059 o

Homework for Wednesday 18 June 2014

Physics: Past Paper 1995 Q.1