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 increase

gradient decrease

negative gradient

positive gradient

zero 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 to north (positive direction)

moving to east (positive direction)

moving to south (negative direction)

Stationary

moving with constant acceleration

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!

Drag labels to their correct position on the image

constant deceleration

zero acceleration

decrease acceleration

constant 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