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