When mastering motion, it's important to understand the differences between scalar and vector quantities. Each graph you encounter will help visualise motion in terms of distance, displacement, velocity, speed and acceleration. Here's a guide to interpreting each graph type with standardised explanations.

**Scalar and Vector Quantities**

##### Scalar Quantities

Have magnitude only.

Examples: distance, speed, mass, temperature.

Example: "The car travelled 50 km."

##### Vector Quantities

Have both magnitude and direction.

Examples: displacement, velocity, acceleration, force.

Example: "The car travelled 50 km to the north."

**Key Definitions**

##### Distance vs. Displacement

Distance: The total path length travelled by an object, regardless of direction. It is a scalar quantity and is always positive.

Displacement: The straight-line distance from the initial to the final position, including direction. It is a vector quantity and can be positive, negative or zero.

##### Velocity vs. Speed:

Speed: The rate at which an object covers distance. It is a scalar quantity and does not include direction.

Velocity: The rate at which an object changes its position, including direction. It is a vector quantity.

**Analysing Motion Through Graphs**

### Distance - Time Graph

##### Gradient (Slope)

Indicates the speed of the object. A steeper slope means higher speed, while a gentler slope means slower speed.

##### Area Under the Graph

Not physically meaningful as the graph already represents distance.

__Interpretation__

##### Purple Line (0 to 4 seconds)

**Curved Line Upwards:** Indicates **acceleration (speeding up)**. The object starts from rest and gradually increases its speed over time, as shown by the curve becoming steeper.

##### Pink Line (0 to 4 seconds)

**Curved Line Downwards:** Represents **deceleration (slowing down)**. The object is reducing its speed as the slope of the curve becomes less steep over time.

##### Black Line (0 to 4 seconds)

**Positive Gradient: This indicates that the object is moving with a constant speed. **

##### Blue Line (4 to 8 seconds)

Horizontal Line: Indicates that the object is stopped (speed is zero). There is no change in distance over time, showing that the object is not moving during this period.

##### Orange Line (8 to 10 seconds)

**Straight Line with a Steeper Slope:** Represents **constant speed**, where the object is moving at a steady rate. The steep slope indicates a relatively faster speed compared to earlier motion (black line), as suggested by the note "Steeper = Faster."

### Displacement - Time Graph

##### Gradient (Slope)

Indicates velocity. A steeper slope means higher velocity.

##### Area Under the Graph

Not relevant in this context.

When the graph is positive, the interpretation is the same as a **Distance-Time Graph**

__Interpretation__

##### Purple Line (0 to 4 seconds)

Curved Line Upwards: Represents acceleration (speeding up). The object starts from rest and its displacement increases at an increasing rate, indicating that its velocity is increasing.

##### Pink Line (0 to 4 seconds)

Curved Line Downwards: Indicates deceleration (slowing down). The object is still moving in the positive direction, but its velocity is decreasing as the slope of the line becomes less steep.

##### Black Line (0 to 4 seconds)

Positive Gradient: This indicates that the object is moving in the positive direction (Forward) with a constant velocity.

##### Blue Line (4 to 6 seconds)

Negative Gradient: This indicates that the object is moving in the opposite direction (backward). The displacement is decreasing, showing that the object is returning towards the reference point. The steepness of the negative gradient suggests that the object is moving backward with increasing speed.

##### Orange Line (6 to 10 seconds)

Horizontal Line: Represents the object being stationary (zero velocity). There is no change in displacement over time, indicating that the object is stationary.

### Speed-Time Graph

##### Gradient (Slope)

Indicates acceleration. A positive slope means speeding up, and a negative slope means slowing down.

##### Area Under the Graph

Represents the total distance travelled.

__Interpretation__

##### Purple Line (0 to 4 seconds)

**Curved Line Upwards:** Represents **increasing acceleration**. The speed is increasing at a changing rate, indicating **non-uniform acceleration**.

##### Pink Line (0 to 4 seconds)

**Curved Line Downwards:** Represents **decreasing acceleration** as the slope is getting less steep. The object is still speeding up, but the rate of increase in speed is slowing down.

##### Black Line (0 to 4 seconds)

**Straight Line with a Constant Gradient:** Indicates **constant acceleration** over this time interval. The speed increases at a steady rate.

##### Blue Line (4 to 6 seconds)

**Horizontal Line:** Represents **constant speed**, meaning there is **no acceleration** during this time interval. The speed remains steady at around 30 m/s.

##### Orange Line (6 to 10 seconds)

**Straight Line Downwards:** Indicates **deceleration (slowing down)**. The speed is decreasing at a uniform rate, suggesting **constant deceleration**

### Velocity-Time Graph

##### Gradient (Slope)

Indicates acceleration. A positive slope indicates acceleration, while a negative slope indicates deceleration.

##### Area Under the Graph

Represents displacement.

When the graph is positive, the interpretation is the same as a **Speed-Time Graph**

__Interpretation__

##### Pink Line (0 to 2 seconds)

**Curved Line Upwards:** Represents **decreasing acceleration**. The velocity is increasing, but at a slower rate as time progresses, indicating that the acceleration is reducing.

##### Black Line (0 to 2 seconds)

**Curved Line Upwards:** Shows **increasing acceleration**. The rate of change of velocity is getting steeper, indicating that the object is speeding up more rapidly.

##### Blue Line (2 to 4 seconds)

**Horizontal Line:** Represents **constant velocity**, meaning the object is moving at a steady speed. The **acceleration is zero** during this time interval, as there is no change in velocity.

##### Orange Line (4 to 6 seconds)

**Straight Line Downwards:** Indicates **constant deceleration**. The velocity decreases at a uniform rate, implying a steady reduction in speed.

##### Purple Line (6 to 10 seconds)

**Straight Line Upwards:** Represents **constant acceleration** again. The velocity increases at a steady rate, meaning the object is speeding up in the positive direction after reaching zero velocity.

##### Area (Displacement)

Area above the time axis (positive velocity) represents displacement in the positive direction.

Area below the time axis (negative velocity) represents displacement in the negative direction.

The net displacement is given by the difference between these two areas.

### Acceleration-Time Graph

##### Gradient (Slope)

Represents the rate of change of acceleration (jerk).

##### Area Under the Graph

Represents the change in velocity over time.

__Interpretation__

##### Pink Line (0 to 2 seconds)

**Straight Line with Positive Slope:** Represents **increasing acceleration**. The acceleration is rising at a constant rate, indicating that the rate at which the object's velocity is changing is becoming faster.

##### Blue Line (2 to 4 seconds)

Horizontal Line: Indicates constant acceleration. The acceleration remains steady at around 40 meters per second squared, meaning the object's velocity is changing at a constant rate during this time interval.

##### Orange Line (4 to 6 seconds)

Straight Line with Negative Slope: Represents decreasing acceleration, transitioning from a positive value to a negative value. This indicates that the object is decelerating, and the rate of deceleration is increasing (acceleration is becoming more negative).

##### Purple Line (6 to 10 seconds

**Straight Line with Positive Slope (from Negative):** Shows **increasing acceleration in the negative direction** initially, then transitioning back towards zero. The object is initially decelerating at an increasing rate, and then the rate of acceleration is reduced towards zero.

## Comments