Speed, velocity and acceleration

1. Scalar quantity

2. Vector quantity

3. Distance

4. Displacement

5. Speed

6. Velocity

7. Acceleration

8. Deceleration

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

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)

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

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.

Equations of motion

1. v = u + at

2. x = ut + 1/2 at2

3. V2 = u2 + 2ax

4. Vavg = V + u2

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

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.

Revision exercise 1.1

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

to the speed.

Time (s)

Distance

(m)

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.

Determine the speed of the truck

a) between 1s and 3sec.

b) between 4s and 6s

Time/s 0 1 2 3 4 5 6

Distance/m 0 10 20 30 40 40 40

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.

example

Exercise

Consider the velocity – time graph below.

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 6 7 8 9

velo

cit

y (

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