Movement and Position (1b)

Unit 1, Topic 2

Average Speed

v equals s/t

Distance-time Graphs

shows how the distance of an object moving in a straight line from a starting position varies with time

also shows:

• constant speed or not

• how large or small the speed is

Constant speed on a DT Graph

• straight line

• slope represents magnitude of speed

• steep slope = very large speed

• shallow slope = small speed

• flat, horizontal line = stationary

Changing Speed on a DT Graph

• changing speed represented by curve

• slope increasing = speed increasing

• slope decreasing = speed decreasing

Calculating Speed from a DT Graph

speed = gradient = Δy (change in d) /Δx (change in t)

Practical (Investigating Motion): Aim

• investigate motion of everyday objects by measuring speed

• ex: paper cone, tennis ball

• measuring speed directly is difficult

• average speed can be calculated by measuring distance moved and time taken

• other methods: light gates to measure speed and acceleration

Practical (Investigating Motion): Variables

• independent: d

• dependent: t

• control: same object for each measurement

Practical (Investigating Motion): Equipment and Purpose

• paper cone/ tennis ball: to measure speed of

• stopwatch: to measure time taken → resolution 1mm

• tape measure/ metre ruler: to measure distance moved → resolution 0.01s

Practical (Investigating Motion): Method

• measure height of 1m with tape measure/ metre ruler

• drop object from this height (distance travelled by object)

• use stopwatch to measure time taken

• record distance travelled and time taken

• repeat 2-3 times and calculate average time taken to fall a certain distance

• repeat for heights of 1.2, 1.4, 1.6 and 1.8m

Practical (Investigating Motion): Result Analysis

• use v=d/t to calculate average speed

  • speed in m/s

  • d in m

  • t in s

Practical (Investigating Motion): Evaluating Experiment

Systematic Errors

• measure at eye level → avoid parallax error

• average reaction time: 0.25s

  • significant when small intervals of time are measured

  • to reduce: use larger distances to have larger time intervals

  • use a ball bearing and an electronic data logger to remove human reaction time error

• use electronic sensors like light gates to obtain very accurate measurements

  • timer starts and stops automatically as it passes sensors positioned at start and stop points

Random Errors

• ensure no draft or breeze because it could affect the falling object’s motion

Practical (Investigating Motion): Safety Considerations

place mat or soft material below falling object to cushion its fall

Acceleration

rate of change in velocity

a = Δv/ t

• a in m/s²

• v in m/s

• t in s

Acceleration vs Deceleration

acceleration can be positive or negative

• speeding up: accelerating positively

• slowing down: decelerating (accelerating negatively)

Velocity-Time Graph

shows how velocity of a moving object varies with time

also shows:

• constant acceleration or not

• magnitude of acceleration

Acceleration on a VT Graph

• straight line = constant

• slope = magnitude

  • steep = large

  • gentle = small

  • positive gradient = increasing velocity

  • negative gradient = decreasing velocity

  • flat line = 0 acceleration (constant velocity)

Calculating Acceleration on a VT Graph

a = gradient = Δy (change in v) / Δx (change in t)

Area under VT Graph

area = distance travelled

Calculating Uniform Acceleration

uniform acceleration = constant acceleration

v² = u² + 2as

• s = d in m

• u = initial v in m/s

• v = final v in m/s

• a = acceleration in m/s²