# 4.3.1 Motion Along a Straight Line

### Displacement, Speed, Velocity & Acceleration

#### Scalar quantities

• Scalar quantities only have a magnitude (size)
• Distance: the total length between two points
• Speed: the total distance travelled per unit of time

#### Vector quantities

• Vector quantities have both magnitude and direction
• Displacement: the distance of an object from a fixed point in a specified direction
• Velocity: the rate of change of displacement of an object
• Acceleration: the rate of change of velocity of an object

#### Worked Example

A car accelerates uniformly from rest to a speed of 150 km h–1 in 6.2 s.

Calculate the magnitude of the acceleration of the car in m s–2. ### Average & Instantaneous Speed

#### Instantaneous Speed / Velocity

• The instantaneous speed (or velocity) is the speed (or velocity) of an object at any given point in time
• This could be for an object moving at a constant velocity or accelerating
• An object accelerating is shown by a curved line on a displacement – time graph
• An accelerating object will have a changing velocity
• To find the instantaneous velocity on a displacement-time graph:
• Draw a tangent at the required time
• Calculate the gradient of that tangent The instantaneous velocity is found by drawing a tangent on the displacement time graph

#### Average Speed / Velocity

• The average speed (or velocity) is the total distance (or displacement) divided by the total time
• To find the average velocity on a displacement-time graph, divide the total displacement (on the y-axis) by the total time (on the x-axis)
• This method can be used for both a curved or a straight-line on a displacement-time graph

#### Worked Example

A cyclist travels a distance of 20 m at a constant speed then decelerates to a traffic light 5 m ahead. The whole journey takes 3.5 s.

Calculate the average speed of the cyclist.

Step 1: Write the average speed equation

Average speed = total distance ÷ total time

Step 2: Calculate the total distance

Total distance = 20 + 5 = 25 m

Step 3: Calculate the average speed

Average speed = 25 ÷ 3.5  = 7.1 m s-1

### Uniform & Non-Uniform Acceleration Graphs

• Three types of graph that can represent motion are displacement-time graphs, velocity-time graphs and acceleration-time graphs

#### Displacement-Time Graph

• On a displacement-time graph:
• The gradient (or slope) equals velocity
• The y-intercept equals the initial displacement
• A diagonal straight line represents a constant velocity
• A positive slope represents motion in the positive direction
• A negative slope represents motion in the negative direction
• A curved line represents an acceleration
• A horizontal line (zero slope) represents a state of rest
• The area under the curve is meaningless
• Remember the displacement-time graph can have positive or negative values on the displacement axis. However, a distance-time graph only has positive Displacement-time graph for different scenarios

#### Velocity-Time Graph

• On a velocity-time graph:
• Slope equals acceleration
• The y-intercept equals the initial velocity
• A straight line represents uniform acceleration
• A positive slope represents an increase in velocity (acceleration) in the positive direction
• A negative slope represents an increase in velocity (acceleration) in the negative direction
• A curved line represents the non-uniform acceleration
• A horizontal line (zero slope) represents motion with constant velocity
• The area under the curve equals the displacement or distance travelled
• Remember the velocity-time graph can have positive or negative values on the displacement axis. However, a speed-time graph only has positive Velocity-time graph for different scenarios

#### Acceleration-Time Graph

• On an acceleration-time graph:
• The slope is meaningless
• The y-intercept equals the initial acceleration
• A horizontal line (zero slope) represents an object undergoing constant acceleration
• The area under the curve equals the change in velocity Acceleration-time graphs for different velocity scenarios ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
Close Close

# ## Download all our Revision Notes as PDFs

Try a Free Sample of our revision notes as a printable PDF.

Already a member?