Scalar vs Vector Quantities

1. Quantities in
Mechanics:
Scalar vs vector
BY TREVOR BENNETT

2. Introduction
 Interestingly, when looking at the topic of quantities in Kinematics, we
always jump to scalar and vector quantities without addressing the
question:
What is a quantity?

3. Quantities

4. Scalar vs Vector quantities
 Scalar – A scalar quantity is a quantity that can be completely
described by a magnitude, that is, by a number and a unit.
Examples of a scalar quantities are mass, length, and time.
 Vector – A vector quantity is a quantity that needs both
magnitude and direction to completely describe it. E.g. velocity

5. Distance
 Distance normally refers to the total distance an
object moves during a particular journey.
 Distance is a fundamental quantity of length. A scalar
quantity.
 Examples of distance are:
 the width of a football field
 The basic dimensions of a cricket pitch

6. Displacement
 Displacement refers to the distance from the starting point at a
particular instant in time. We normally use s for displacement
(which is pretty silly, since s looks like it should stand for
speed, but doesn't).
 When ever a body moves from one position to another it
undergoes a displacement.
@ t = 0
s
@ t = 1s
@ t = 4s

7. Speed vs
 Some people say that speed and velocity are
similar but say you?
 Speed tells us how fast something is moving. Speed is all about the rate
at which a body or object can cover a particular distance over a period of
time. Speed is the ratio of the fundamental quantity of length to the
fundamental quantity of time. Speed =L/T where L is length and T is time
 A man running at 10 km/h is speed which is scalar
 The diagram shows a graph of distance vs time.
 The line on the graph represents constant speed

8. Speed : High and Low

9. Velocity
 Velocity is a vector quantity which refers to "the rate
at which an object changes its position." Velocity is a
ratio of displacement to time
 We can also write the velocity using delta notation:
 The diagrams show high a low velocity.

10. Examples of speed and velocity
 According to Top End Sports (2018), the
day after Usain Bolt's 9.58 100m world
record, the IAAF released details of the split
times for that race. The time for each 20m
distance of the race was recorded. For Bolt,
the fastest interval (60m to 80m) was run at
an average speed of about 45 km/hr,
12.42 m/s).
An example of velocity is when the universe
boss, Chris Gayle, hits a ball at a rate of 65
mph over deep midwicket. Here, there is
magnitude and direction.


11. Examples of speed and velocity
 A car travelling at 150 mph that is considered to high
magnitude, which is speed: very dangerous speed
 Now if the car is going around corner, it is considered to be
velocity. Why? Because direction keeps changing.

12. Scalar
quantities
 Mass
 Length
 Time
 Density
 Speed
 Area
 volume

13. Vector Representation
 A vector quantity can be represented graphically by a line so that
 (a) the length of the line denotes magnitude of the quantity
 (b) the direction of the line give a sense of where it is going by the arrow
head.
 The vector AB is referred to as
 The magnitue is written

14. Vector Algebra

15. Attention quiz
d – c = a – b Is this vector algebra
correct

16. That’s all for now
folks!