2.1Distance 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, (b)its displacement.

|(a) Distance covered = 5 + 3 = 8 km |[pic] | |(b) Displacement = 5 – 3 = 2 km due east of starting point. | |

2.2Speed and Velocity (Text pg 48: Unit 3.2)

Vectors and Scalars

• scalars – magnitude ONLY

• vectors – magnitude + direction

Speed

• 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

Total time

• SI unit : metre per second (ms-1)

• 1 ms-1 = km h-1

=

Example 2

In the 1988 Seoul Olympics, Ben Johnson broke the world record to run 100 metres in 9.83 seconds. What was his average speed?

Average speed= 100 / 9.83

= 10.2 ms–1

Velocity

• 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

Example 3

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 (b)the average velocity.

(a)Average speed= total distance covered / total time taken

= 8 / 0.2

= 40 km h–1

(b)Average velocity= total displacement / total time taken

= 2 / 0.2

= 10 km h–1 due east of starting point O.

2.3Displacement–Time graphs

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.

Example 4

(a)What is the displacement at (i)t = 3s?

(ii)t = 15s?

(iii) t = 18s?

(b)What is the velocity at (i)t = 3s?

(ii)t = 15s?

(iii) t = 18s?

2.4Acceleration

6. Defined as the rate of change of velocity. Direction of acceleration is the direction of change in velocity. Acceleration = Final velocity – Initial velocity

Time

a =v – u

t

a: acceleration v: final velocity t: time u: initial velocity 7. SI unit: ms–2

8. Negative acceleration = deceleration / 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. | |

Average acceleration= (20 – 0) / 10

= 2 ms–1 due...