This document defines key concepts related to motion, including scalar and vector quantities, distance, displacement, speed, velocity, acceleration, and deceleration. It provides equations of motion and examples to calculate speed, acceleration, distance, and time using graphs of distance-time and velocity-time. Speed is defined as distance divided by time, while velocity includes direction and can be determined from the slope of a velocity-time graph or by the change in velocity over time.

1. Speed, velocity and acceleration
by: Chris Lembalemba
(chrislembalemba@yahoo.com)

2. 1. Scalar quantity
2. Vector quantity
3. Distance
4. Displacement
5. Speed
6. Velocity
7. Acceleration
8. Deceleration

3. Definitions
1. Scalar quantity: a quantity that has only magnitude.
E.g. mass, temperature, distance e.t.c.
2. Vector quantity: a quantity that has both
magnitude and direction e.g. weight, displacement,
force, acceleration e.t.c.
3. Distance: this is the amount of space between two
points. It is a scalar quantity and measured in meters,
centimeters, kilometers, miles, light years e.t.c. The SI
unit is meter (m).
4. Displacement: This is distance in a particular
direction. E.g. 5km North, 15centimeters West

4. 5. (a) Speed: this is distance covered per unit time.
It is a scalar quantity and is measured in meters per
second (m/s), kilometers per hour (km/h), e.t.c. The
SI unit for speed is meter per second (m/s).
speed= distance (m)
time (sec)
(b) Average speed: this is given by:
average speed = total distance (m)
total time taken (s)

5. 6. Velocity: … is displacement per unit time. It is
also defined as distance covered in a particular
direction per unit time OR speed in a particular
direction. It is a vector quantity and is measured in
meters per second (m/s).
For motion in a straight line, + or – is used to indicate
direction:
+10 m/s
- 10 m/s

6. 7. Acceleration: this is change of velocity per
unit time. It can also be defined as the rate change
of velocity. It is a vector quantity. The SI unit is
meters per second squared (m/s2) or (ms-2)
8. Deceleration: this is a negative acceleration.
It is also called retardation.

7. Equations of motion
1. v = u + at
2. x = ut + 1/2 at2
3. V2 = u2 + 2ax
4. Vavg = V + u
2
5. Sp. = D/t
Where;
v = final velocity
u = initial velocity
vavg = average velocity
a = acceleration
t = time
x = displacement
Sp. = Speed
D = Distance
t = time

8. Examples
1. A car travels 600m in 30s. What is its average
speed?
2. A car has a steady speed of 8m/s.
a) How far does the car travel in 8s?
b) How long does the car take to travel 160m?
3. A car takes 8s to increase its velocity from 10m/s to
30m/s.
a) What is its acceleration?
b) Calculate the distance covered.
c) Determine its average velocity.

9. Revision exercise 1.1

10. MOTION GRAPHS
1. Distance – time
graphs
- The distance
covered by a car can
be measured every
second. This can be
represented on a
graph.
- On a graph, the y-axis
is the distance
and the x-axis is the
time taken.
- The gradient is equal
Time (s)
Distance
(m)

11. Exercise
The distance traveled by truck was measured at
intervals. The information was recorded in the table
below. Use the information to draw a distance – time
graph.
Time/s 0 1 2 3 4 5 6
Distance/m 0 10 20 30 40 40 40
Determine the speed of the truck
a) between 1s and 3sec.
b) between 4s and 6s

12. 2. Velocity – time graphs
- For the speed time graph, velocity is on the y-axis
and time on the x-axis.
- The gradient of the graph is equal to the
acceleration.
Time (s)
Velocity
(m/s)
The area under the graph is equal to the distance covered.

13. example

14. Exercise
Consider the velocity – time graph below.
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9
velocity (m/s)
time (s)
1. Calculate the acceleration during the first 2 seconds.
2. What is the acceleration between the 2nd and 4th seconds of the motion?
3. Determine the deceleration.
4. Calculate;
a. Distance covered in the first 2 seconds
b. Total distance covered
5. Total distance covered