# 3.1.1 Displacement, Velocity & Acceleration

### 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. #### 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

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