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Kinematics . Displacement, Velocity and Acceleration. Mechanics: The study of how matter and forces interact, on a macroscopic scale. Kinematics: The part of mechanics concerned with the study of motion, without consideration of its causes. Dynamics:

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kinematics

Kinematics

Displacement, Velocity and Acceleration

slide2

Mechanics:

The study of how matter and forces interact, on a macroscopic scale.

Kinematics:

The part of mechanics concerned with the study of motion, without consideration of its causes.

Dynamics:

The part of mechanics concerned with the study of motion and its causes, notably forces.

slide3

Compare and Contrast

Position:

Where you are from a reference point. Think about an axis scale. Considered a vector; unit is meters.

Distance:

The total “ground” travelled. Does not matter where you start. Always increasing in the positive direction. Scalar quantity; unit is meters.

Displacement:

Based on position. How far you travelled with respect to your reference point. Start to finish. ∆s = sf – si. Vector quantity; unit is meters.

slide4

Kinematics

  • Speed and Velocity
  • Both are measured in ms-1
  • Speed is a scalar while velocity is a vector
  • These are both averages as they may vary over the period of time taken.
  • Note:Many of the examples we study involve linear motion: things moving in straight lines. Also, the direction is not always stated for a vector quantity if it is clear.

Average Speed = Distance travelled

Total time

v = s

t

Average Velocity = Change in displacement

Total time

v = ∆s

∆t

slide5

Q. Arthur takes a walk from home, around the park and back to where he started. If he walked 2.7km over fifteen minutes, determine…

  • his distance travelled.
  • his total displacement.
  • his average speed.
  • his average velocity.

= 2700 m

= 0

= 3 ms-1

= 0

slide6

Frames of Reference

Measurements can be made from different viewpoints, known as ‘frames of reference’.

E.g. To an observer, a building appears to be at rest. However to a driver of a passing car, the building appears to be moving away at high speed. The stationary observer, and the driver of the car, both have a different frame of reference.

Frames of reference link

slide7

Relative Velocity

If two moving objects have different velocities, their relative velocity depends upon which frame of reference you are using.

If we know the velocities of two bodies in the same frame of reference, the velocity of body A with respect to body B is given by…

vAB = vA - vB

E.g. Car X moves at 20ms-1 to the left, car Y at 16ms-1 to the right. What is the velocity of X with respect to Y?

(taking to the left as the +ive direction)

vXY = vX – vY = 20 - (-16) = 36ms-1

slide8

Acceleration

Acceleration is what happens when the velocity of a body changes. It is a vector quantity.

Q. Rearrange this formula to make v, u and t the subjects.

Average Acceleration = Change in velocity

Total time taken

a = v – u

t

a = ∆v

∆t

or

( v = final velocity, u = initial velocity )

slide9

Some typical apparatus for linear motion experiments:

  • One light gate and a double interrupter card
  • Two light gates and a 10cm card.
  • Ticker timer
  • Distance sensor, interface and computer
  • Stopwatch
  • Trap door and digi-timer