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Linear Motion

A scalar has only magnitude but without direction (and hence cannot be resolved into components).

A vector has both magnitude and direction (and hence can be resolved into components).

Distance is a scalar, measured in m, km, cm etc.

(1 km = m, 1 m = cm)

Example 1:

Distance travelled from A to B:___________________m

Displacement is a vector also measured in m, km, cm

: Magnitude is measured from initial position to final position

: Direction is measured from initial position to final position

From the above example:

Magnitude of displacement travelled from A to B:__________m; its direction: __________

Example 2:

What is the total distance covered if one travels a complete square starting from A?

What is the total displacement if one travels a complete square started from A?

Example 3: Study the following case: (The speed is uniform within each time interval.)

i) A car takes 12 s to move 100 m.

ii) Then it remains stationary for 2 s.

iii) It takes another 12 s to return to the stating point.

iv) It takes further 6 seconds to move negative 15 m.

Complete the following table and sketch the displacement-time graph

| |unit |i |ii |iii |iv |Whole journey |

|distance |m | | | | | |

|displacement |m | | | | | |

|Time taken |s | | | | | |

|Average speed |ms-1 | | | | | |

|Average velocity |ms-1 | | | | | |

Note:

1. 1 m s-1 = km h-1

2. Area of the graph under the curve has no physical meaning.

3. Slope of the tangent at a point to the graph =

Example 4: In the same case of example 3:

a. Sketch the speed time graph:

b. Sketch the velocity time graph (paying attention to the sign of the direction).

c. What is the average velocity in region i)?

d. What is the average velocity of the whole journey?

e. What is the instantaneous velocity when t =5s ?

Study the following graph:

Instantaneous Velocity

Velocity – time graph

Example 5:

Total displacement (area under line):_____________ m

Average velocity (total displacement/time taken):_______________( )

Average speed:_________________

Instantaneous velocity (P. 21 Instantaneous speed) when t = 3s:_____________

Example 6:

Total displacement (area under line):_____________ m

Average velocity:_______________( )

Average speed:_________________

Instantaneous velocity (P. 21 Instantaneous speed) at t = 3s:_____________

Acceleration: a =[v(instantaneous) – u(instantaneous)]/t(time taken for the change)

Acceleration in case I (ie slope of v-t graph):________________

Acceleration in case II (ie slope of v-t graph):________________

4 cases in acceleration: (DEFINE: Positive direction to the right)

|case |v |a |

|a |+ |+ |

|b |+ |- |

|c |- |+ |

|d |- |- |

Let the initial speed = 5 m s-1and magnitude of acceleration = 2m s-2

Case a:

|t /s |0 |1 |2 |3 |4 |

|v /ms-1 | | | | | |

Case b:

There exists a U turn!

Case c:

There exists a U turn!

Case d:

-----------------------

10m

10m

10m

B

A

10m

10m

10m

10m

A

10

t /s

25

v /m s-1

What is the average velocity? ______________

What is the instantaneous velocity when t = 5s?, _____________ 10s?______________

Note: instantaneous velocity `"average velocity

v / ms-1

8

t/s

10

v / ms-1

10

8

t/s

Pge velocity? ______________

What is the instantaneous velocity when t = 5s?, _____________ 10s?______________

Note: instantaneous velocity ≠average velocity

v / ms-1

8

t/s

10

v / ms-1

10

8

t/s

Positive direction to the right

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