Average speed is the ratio of the distance covered to the time taken to cover a distance OR Average speed is the rate at which distance changes. Or
Distance travelled divided by the total time taken. Average speed
V
The word rate implies that “one divides by time”.
When we take a reading on the speedometer of a motor car we are travelling in, we obtain the speed of the car at that moment. We call this the instantaneous or momentary speed. The SI unit for speed is m.s-1. Speed is a scalar quantity therefore it does not have direction.
Velocity, average velocity and instantaneous velocity
Average velocity is the ratio of the displacement undergone to the time taken to undergo this particular displacement. OR Average Velocity is the rate of change of displacement. OR Average velocity is the displacement (change in position) divided by time taken.
Average speed
V
Average velocity is a vector quantity therefore it has both magnitude and direction The SI unit for velocity is m.s-1.
Instantaneous speed and instantaneous velocity
Instantaneous (momentary) velocity is the velocity at which an object moves at a particular moment in time (speed measured over extremely short time interval. Or the displacement divided by an infinitesimal (very small) time interval.
Activity 3E
3.1 Give the synonyms or one word for the followings: i) “Momentary”………
ii) “Very small”………. 3.2 Which words in the notes mean:
i) One divides by time………. ii) The ratio of distance and time……… iii) The ratio of displacement and time…………...
iv) The speed of an object at that moment……….. 3.3 The SI unit for velocity and speed is……… 3.4 Complete the following sentences:
i) Speed is a ………. quantity while velocity is a ………. quantity.
ii) This implies that velocity has both magnitude and ……… 3.5 State whether the following statement is true or false:
“Speed and velocity are similar because both of them are measuring how fast an object is moving and that is why they are measured in m.s-1”……….
ACTIVITY 3
Average speed and Instantaneous speed 1. Define the following concepts
1.1 Average speed 1.2 Average velocity
1.3 Instantaneous speed 1.4 Instantaneous velocity
1.5 Give the synonym for the word “instantaneous.
2. Tom and Sally are on a cycling tour. They set out one morning from the camping site along the following
6km North, 4km East, 3km South, 4km East, 6km South, 4km East and 3km North 2.1 Draw in the frame below, a scale diagram (where every 1cm=1km) to show the route that
the followed in the seven stages of the cycling tour. Start your diagram at the point indicated.
2.2 What is the total distance covered by Tom and Sally (1) in km and (2) in m?
North ↑
2.3 Use different coloured pencils to indicate and measure Tom and Sally’s displacement at the end of the route, measured from the camping site (1) in km and (2) In m.
2.4 Explain the difference in between the distance covered and the displacement at the end of the route.
2.5 The journey along the route takes them 2 hours. Calculate their average speed for the total route in km.h-1 and in m.s-1.
2.6 Calculate the average velocity for the total route in km.h-1 and m.s-1.
3 A number of athletes are competing in a 400m race.
3.2 Calculate the how long it takes another sprinter to complete a 400m race with an average speed of 8m.s-1.
4 A person walks 90m due east and then turns around and walks 18m towards the starting point. The time taken is 2minutes.
4.1 Draw a vector diagram to illustrate the person’s change in position. Use the tail to head method and the scale of 10m=1cm.
4.2 Compare the distance walked with the person’s displacement from the starting point. (Write down the value of distance and displacement)
UNIT 4: ACCELERATION
An object accelerates when a change in its velocity occurs. For example change in speed or change in direction of the movement. Acceleration can be defined as follows:
Acceleration is the rate at which velocity changes or Acceleration is the rate of change of velocity
An object accelerates if:
The magnitude of its velocity changes (e.g. if the velocity increases or decreases
The direction of movement changes.
The term acceleration is not only used when the velocity of an object increases, but also in situations in which the velocity decreases.
When acceleration is to be determined; it is necessary to measure the initial velocity and the final velocity as well as the time taken for the velocity change.
The acceleration of an object can calculated as follows:
Where:
a= average acceleration (in short acceleration) in m.s-2 ∆v=change in velocity in m.s-1
∆t= change in time in s Vi= initial velocity in m.s-1 Vf= final velocity in m.s-1
Acceleration is a vector quantity.
Acceleration is measured in metres per second squared (m.s-2) Positive and negative acceleration
A positive value for acceleration indicates that the acceleration is in the same direction as the movement. Then velocity increases.
Negative value for acceleration indicates that the acceleration is in the opposite direction to the movement. Then the velocity decreases.
Constant or uniform acceleration
Activity 4E
4.1 Circle the correct answer in the following: i) An objects accelerate when:
A Displacement changes B Time changes
C Change in velocity occurs
ii) The rate at which velocity changes is: A Acceleration
B Displacement C Speed
D Distance
iii) The SI unit for acceleration is:
A m
B Kg
C m.s-2 D m.s-1
iv) Positive acceleration indicates that: A Acceleration is bigger
B Acceleration is in opposite direction C velocity is decreasing
D acceleration is in the same direction as the movement 3.2 Give the symbol of the following:
i) Final velocity……… ii) Change in velocity……….. iii) Average acceleration………… iv) Initial velocity………..
v) Change in time………
4.3 Give the synonym for “constant”………. 4.4 Give the antonym for “positive”………
ACTIVITY 4