Kinematic Equations and Graphs

Graphs of Motion

​Graph is a horizontal line (zero gradient)

Displacement is constant for every second

Displacement–Time Graphs Object at Rest

​Graph is a straight line with constant gradient

Displacement increases by 25 m every second

​​Displacement–Time Graphs

(Object at Uniform (Constant) Velocity)

​Graph has an increasing gradient

Velocity increases

​​Displacement–Time Graphs

(Object at Increasing (Non-uniform) Velocity)

​Graph has a decreasing gradient

Velocity decreases

Displacement–Time Graphs

(Object at Decreasing (Non-uniform) Velocity

Labelling

label section based on motion!

Region A
Region B
Region C
Region D-E

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gradient decrease

negative gradient

zero gradient

gradient increase

positive gradient

Labelling

For a car moving on straight road, assign

its reference point: at X (0 m);

its direction: taking due east of X as positive.

label point B, D, and G

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moving to west (negative direction)

moving with constant acceleration

Stationary

moving to south (negative direction)

moving to east (positive direction)

moving to north (positive direction)

Dropdown

The displacement−time graph below shows how the motion of an object changes with time.

From t = 0 s to t = 20 s, ​ the object moves with ​

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From t = 20 s to t = 30 s, the object ​

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From t = 40 s onwards, the object ​

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Dropdown

Fig shows the distance-time graph for the journey of a cyclist. Describe the motion of the cyclist in the time between:

1. time = 0 and time = 15s ​

​

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2. time = 15s and time = 30s ​ ​

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3. time = 30s and time = 40s ​

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​The velocity−time graph shows

a horizontal, straight line;

uniform velocity
zero acceleration.

​​Velocity–Time Graphs

(Object at Uniform Velocity)

​The velocity−time graph shows

that velocity increases by 10 m s⁻¹ every second;

a positive and constant gradient (constant acceleration).

​​Velocity–Time Graphs

(Uniform Acceleration)

​The velocity−time graph shows

that velocity decreases by 10 m s−1 every second;

a negative and constant gradient (constant deceleration).

Velocity–Time Graphs

Uniform Deceleration

​The velocity−time graph shows

that the increase in velocity increases with time;

a positive and increasing gradient;

increasing acceleration.

Velocity–Time Graphs

(Increasing Acceleration)

​The velocity−time graph shows

that the increment in velocity decreases with time;

a positive and decreasing gradient;

decreasing acceleration.

​Velocity–Time Graphs

(Decreasing Acceleration)

Labelling

label section based on motion!

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constant deceleration

zero acceleration

constant acceleration

decrease acceleration

Dropdown

Look at the picture!

motion from O to A is ​

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, with ​

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m/s² of acceleration

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Look at the picture!

motion from A to B is ​ ​

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with ​

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. We can identify it by the ​

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gradient on the graph

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Look at the picture!

motion from B to C is ​

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. The acceleration is ​

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m/s²

Dropdown

Look at the picture!

motion from C to D is ​

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. Acceleration of object is ​ ​

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m/s²