2: SPEED, VELOCITY AND ACCELERATION
Distance and Displacement
• Distance is the total length covered by a moving object irrespective of the direction of motion, i.e. only the magnitude is of importance. • Displacement is the distance measured in straight line AND in a specific d__________________. Both magnitude and d_________________ are important. Example 1
A car travels 5 km due east and makes a U-turn back to travel a further distance of 3 km. Find
(a) the distance covered,
|(a) Distance covered = 5 + 3 = 8 km |[pic] | |(b) Displacement = 5 – 3 = 2 km due east of starting point. | |
Speed and Velocity (Text pg 48: Unit 3.2)
Vectors and Scalars
• scalars – magnitude ONLY
• vectors – magnitude + direction
• defined as the rate of change of distance, in other words, distance moved per unit time • instantaneous speed: speed at that particular instant
Average speed = Total distance
• SI unit : metre per second (ms-1)
• 1 ms-1
= km h-1
In the 1988 Seoul Olympics, Ben Johnson broke the world record to run 100 metres in 9.83 seconds. What was his average speed?
= 100 / 9.83
= 10.2 ms–1
• Defined as the rate of change of displacement. It is speed in a specific direction. • When asked for the velocity of an object, have to state the speed and direction of the object. • 2 cars may have the same speed but different velocity.
• Negative sign indicates opposite direction
If the time taken for the car in example 1 to move from O to E is 0.2 hour, calculate (a)
the average speed and
the average velocity.
= total distance covered / total time taken
= 8 / 0.2
= 40 km h–1
= total displacement / total time taken
= 2 / 0.2
= 10 km h–1 due east of starting point O.
1. displacement –- distance in a certain direction.
2. The gradient of s–t graph is the velocity of the object. 3. A positive gradient of the displacement–time graph indicates that the object is moving in the same direction as the displacement. 4. A negative gradient of the displacement–time graph indicates that the object is moving in the opposite direction to the displacement. 5. A zero gradient of the displacement–time curve indicates that the object is stationary.
What is the displacement at
t = 3s?
t = 15s?
(iii) t = 18s?
What is the velocity at
t = 3s?
t = 15s?
(iii) t = 18s?
6. Defined as the rate of change of velocity. Direction of acceleration is the direction of change in velocity.
= Final velocity – Initial velocity
v – u
a: acceleration v: final velocity t: time u: initial velocity 7. SI unit: ms–2
8. Negative acceleration = decelera
tion / retardation
9. If an object is moving in a straight line, but changes its speed, it is accelerating. (such as in a 100 m sprint) 10. If an object is moving at constant speed but changes its direction as it moves (such as whirling a stone attached to a string), it is accelerating.
|Example 5 |[pic] | |A bus starts from rest and achieves a velocity of 20 ms–1 (72 kmh–1) in 10 s while| | |moving westwards from a starting point O. Calculate its average acceleration. | |
= (20 – 0) / 10
= 2 ms–1 due...
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