Linear Velocity and Acceleration

KINEMATICS - this is the study of VELOCITY and ACCELERATION without reference to the
forces causing motion.

LINEAR VELOCITY AND ACCELERATION

1. SYMBOLS USED - these are shown below and are all lower case letters. It may be found
useful to remember that they form a word pronounced "stoova".

SYMBOL MEANING UNITS

s Distance and displacement metres (m)

t Time taken seconds (s)

u Initial velocity metres per second (m.s-1)

v Final velocity and
average velocity metres per second (m.s-1)

a Acceleration and metres per second
deceleration or retardation per second (m.s-2)

2. DISTANCE/DISPLACEMENT - distance is the actual distance between two points whereas.
displacement is the direct, or straight line, distance between them. Hence the magnitude of
these two quantities may well be different. For example a car travelling along a curved road
moves through a distance shown by the
dotted line but the displacement or direct ACTUAL DISTANCE
distance between A and B is shorter.

Displacement is a VECTOR QUANTITY
since both its MAGNITUDE and DIRECTION
are known.
A B
DIRECT DISTANCE
Unit Conversion m = km x 1000
m = mm ÷ 1000

3. VELOCITY - for any object to have velocity it must be moving, in other words its
displacement must be changing over a period of time. Velocity is defined as the RATE OF
CHANGE OF DISPLACEMENT. Velocity is a vector quantity and is often incorrectly
referred to as SPEED (see note after example 1 on page 2).

 VELOCITY = RATE OF CHANGE OF DISPLACEMENT

= DISPLACEMENT
TIME

 v = s (m s-1)
t

Unit Conversion m s-1 = km h-1 x 1000
3600

m s-1 = m min-1  60




1

,EXAMPLE 1 - consider the situation where a motor car:

 accelerates away from a road junction and reaches a certain speed then travels at this speed
for a while before slowing down (i.e. decelerating) at the next junction.

If the road junctions are 600 metres apart and the total time taken is 20 seconds determine the
average speed.

This answer, although useful, tells us nothing about:

 the MAGNITUDE of the maximum speed of the car or
 the DIRECTION the car was travelling.

Because of this AVERAGE SPEED is referred to as a SCALAR QUANTITY and can be defined as
actual distance travelled per unit time.

EXAMPLE 2 - a motor car starts a journey at point A and completes it at point E.

A B C D E

Using the information given in the table below determine:
(a) the average speed between each of the points
(b) the total distance travelled
(c) the total time taken for the journey
(d) the average speed for the whole journey

SET OUT ALL CALCULATION WORK AND THEN COMPLETE THE TABLE BELOW.

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DISTANCE TIME TAKEN AVERAGE SPEED
BETWEEN BETWEEN BETWEEN
(s - metres) (t - seconds) (v - m s-1)

A-B 60 6

B-C 40 2

C-D 96 3

D-E 60 5

A-E




2

, The variation of displacement with time (i.e. velocity) may be represented graphically as shown.
This variation can be in any one of four forms:




DIPLACEMENT
I. INCREASING VELOCITY (i.e. ACCELERATION)
II. CONSTANT VELOCITY
III. DECREASING VELOCITY (i.e. DECELERATION)
IV. ZERO VELOCITY (i.e. STATIONARY)

Note - the slope, or gradient, of a DISTANCE - TIME
GRAPH gives the ………………………………………
TIME

EXAMPLE 3 - Planet Earth as a diameter of approximately 13 000 km and a satellite orbits it once
every 90 minutes at an altitude of 500 km above the earth's surface. Determine the velocity of the
satellite in km per h.
If Earth is 150 000 000 km from the sun and takes 365 days to complete one orbit determine its
velocity in km per day and km per h.

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