# Motion

The motion (movement) of an object, such as a car or a ball, is described in terms of its speed and its acceleration.

# Concept 1: Speed

## Success Criteria

• I can define ‘speed’ and 'velocity'.

• Use formulae to calculate speed, distance, and time.

• State the SI units for speed, distance, time and acceleration.

Energy

Joule

Transformation

## Speed vs Velocity

Success Criteria:
I can
define ‘speed’ and 'velocity'. Speed refers to how fast an object is travelling. It is measured in units like meters per second (m/s) or kilometers per hour (km/h).

• To change from km/h to m/s: multiply by 1000, then divide by 60 divided by 60

• To change from m/s to km/h: divide by 1000, then multiply by 60 x 60

Velocity is the speed with the direction specified.  Above: Speed of 50 km/h means the car is travelling at a rate of 54 km every hour.

The car's velocity is 50 km/h east.

Above: Speed of 5 m/s means that the cyclist is travelling at a rate of 5 m every second.'

Velocity is 5 m/s north.

## Instantaneous vs Average Speed

Success Criteria:
I can define ‘speed’ and 'velocity'.

### Instantaneous speed

An object's instantaneous speed is the speed at one instant in time.

An object travelling in a straight line with a constant speed will have no net force acting on it.

An object travelling in a straight line with a changing speed will have a net force acting on it.

### Average speed

Average speed (v) is the distance travelled divided by the time taken.

The units used must be consistent for speed, distance, and time.  Above: An object travelling in a straight line with a constant speed will have no net force acting on it.

Above: An object travelling in a straight line with a changing speed will have a net force acting on it.

## Task 1: Complete the following:

• Page 9 - Units of Speed

• Page 10 - Calculating Speed

• Page 11 - Using Formula Triangles

• Page 12 - More Speed Calculations

### Education Perfect

Complete the task called "1.1 Concept 1: Speed"  # Concept 2: Distance-Time Graphs

## Success Criteria

• Use a distance-time graph to describe the motion of an object.

• Calculate the speed of an object using the gradient of a distance-time graph.

## Vocabulary

Energy

Joule

Transformation  A distance-time graph shows how an object's distance changes over time.

• A straight line on a distance-time graph shows the speed is constant.

• A flat line means the object is stationary, at constant 0 speed.

• The steeper the line, the faster the speed

• A curved section shows the speed is changing.

• A curve upward shows acceleration

• A curve downward shows de

The motion of an object can be described from a distance-time graph: Describing the motion of the green car:

The green car travels at a constant speed between 0 and 5 seconds. It stops at 5 seconds and is stationary until 12 seconds.

Describing the motion of the blue car:

The blue car travels at a constant speed between 0 and 5 seconds. It stops at 5 seconds and is stationary until 9 seconds. At 9 seconds, the car turns around and travels at a constant speed to the start.

Describing the motion of the red car:

The red car is stationary until 2 seconds. From 2 seconds until 6 seconds, the car's speed is increasing (acceleration). It travels at a constant speed between 6 and 7.5 seconds. From 7.5 seconds until 10 seconds, the car's speed is decreasing (deceleration). It stops at 10 seconds, and is stationary until 12 seconds.

The gradient of a distance-time graph gives the speed of the object.

• A positive speed value shows motion in the direction away from the start point.

• A negative speed value shows motion in the direction towards the start point. ### How to calculate average speed

Average speed is the speed that has been travelled on average over the entire distance.

In a car, the odometer measures instantaneous speed. This is the speed that the car is travelling at in that particular moment.

The average speed a car may have been travelling at for a journey from Cambridge to Hamilton may have been 70km per hour but at some times they may have been travelling at 100km per hour and at other times, they may have been travelling at 45km per hour.

We use the symbol ∆ to mean, “change in”. So using the formula, we calculate the average velocity by dividing the change in distance by the change in time taken. ## Task: Analyse these Distance-Time Graph simulations

• Page 13 - Distance-Time Graphs

• Pages 14-15 - Team New Zealand Secondary Schools

• Page 16 - Calculating Speed from a Distance-Time Graph

• page 17 - New Zealand Secondary Schools Rally Team

Motion > Distance-Time Graphs  ### Education Perfect

Complete the task called "1.1 Concept 2: Distance-Time Graphs" # Concept 3: Acceleration

## Success Criteria

• I can define ‘acceleration’

• I can use formulae to calculate acceleration, change in speed, or change in time.

## Vocabulary

Energy

Joule

Transformation Acceleration is how quickly the motion is changing.

Units are a speed unit divided by a time unit. Positive acceleration means the object is speeding up. Negative acceleration (deceleration) means the object is slowing down. ### Average acceleration

Average acceleration (a) is the overall change in speed, divided by the time taken.

The units must be consistent for speed, time, and acceleration. If an object is accelerating, then there is a net force acting on the object. • Page 18 - Acceleration

• Page 19 - Acceleration Problems

Go to Motion > Distance-Time Graphs, and complete the tasks on there.  ### Education Perfect

Complete the task called "1.1 Concept 3: Acceleration" # Concept 4: Speed-Time Graphs

## Success Criteria

• I can use a speed-time graph to describe the motion of an object.

• I can calculate acceleration using the gradient of a speed-time graph.

• I can calculate distance travelled from the area under a speed-time graph.

## Vocabulary

Energy

Joule

Transformation

A speed-time graph shows how an object's speed changes over time.

• A flat line on a speed-time graph shows that the speed is constant (no acceleration).

• A sloping line shows that the acceleration is constant. The motion of an object can be described from a speed-time graph.

Watch this video below to learn how to describe each section of a speed-time graph. ### Calculating acceleration from a speed-time graph

The gradient of a speed-time graph gives the acceleration of an object.

### Calculating distance travelled from a speed-time graph

The area under a speed-time graph gives the distance travelled by the object.  ## Task: Revising and comparing distance-time graphs and speed-time graphs

Learn to connect position-time and velocity-time graphs. Explore velocity using an animated car icon connected to either a position-time or a velocity-time graph, or both. Then investigate other motion graphs.

Move the little man on the screen and view the resulting graphs of position (distance), velocity, and acceleration. Explore why the graphs follow predictable patterns. Set initial conditions and view the graphs simultaneously as the "Moving Man" changes position. You can also program the motion by entering an equation for the position as a function of time and play it back in slow motion or at real speed. Note: For introductory explorations, you can “uncheck” the Acceleration vs. Time graph

• Page 20 - Speed-Time Graphs

• Page 21 - Calculating Acceleration from a Speed-Time Graph   