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MOTION

DISTANCE & DISPLACEMENT

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Distance (d) - numerical measurement of the length between two objects or points

  • scalar quantity

  • SI unit is meter (m)​

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Displacement (s) - the shortest distance from the origin point to the final destination

  • vector quantity

  • SI unit is meter (m)

 

If an object moves forward from the origin point 3 centimeters, back 2 centimeters, and forward 6 centimeters, the distance travelled by the object is 11 centimeters; if an object moves forward from the origin point 3 centimeters, back 2 centimeters, and forward 6 centimeters, it has been displaced by 7 centimeters to the right.

SPEED & VELOCITY

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Speed - the rate at which an object covers distance; a quantity that can be used to describe how fast or slow an object is moving

  • scalar quantity ​

  • SI unit is meters per second (m/s)

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Velocity (v) -  used to describe how fast or slow an object is moving in a given direction; the rate at which an object is moving in a given direction

  • vector quantity ​

  • SI unit is meters per second (m/s)

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If an object is moving an average of 10 kilometers every 20 minutes, the object’s speed is 30km/h; if an object is moving an average of 10 kilometers north every 20 minutes, the object’s velocity is 30km/h north-bound.

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The velocity of an object is likely constantly changing. This is why we refer to velocity as either:

  • Instantaneous velocity - the velocity of an object at any given moment

  • Average velocity - the average velocity of an object over any given period of time

ACCELERATION​

 

Acceleration (a) - the rate at which the velocity of an object changes over a period of time

  • vector quantity

  • SI unit is meters per seconds-squared (m/s^2)

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When finding instantaneous acceleration, time is equal to zero; this is not the case for the process of finding average acceleration. 

EQUATIONS OF MOTION

 

Conditions for using the equations of motion:

  • All quantities must be in SI units 

  • motion must be linear

  • acceleration must be constant

FREEFALL MOTION

 

Freefall motion - any motion of a body in which gravitational force is the only force acting on it, unless stated otherwise

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In freefall motion, objects accelerate towards the ground; that acceleration has varying values at different places in the universe.

 

On Earth, the gravitational field strength is 9.8 m/s^2 - this means that, assuming there is no effect of resistive force, the speed of the freely falling object would increase by 9.8 m/s every second. 

MOTION GRAPHS

 

Motion graphs can be used to

  • Depict motion visually

  • Calculate kinematic variables

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In most (if not all) motion graphs, time will always be shown on the x-axis. The x-axis usually represents the independent variable, whereas the y-axis shows the dependent variable. 

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The important features of any motion graph that you may be asked to find are the gradient and the area under the graph.

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There are many types of motion graphs:

  1. Position-time graph

  2. Distance-time graph

  3. Velocity-time graph

  4. Acceleration-time graph

POSITION-TIME GRAPHS

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In a position-time graph, the gradient is the velocity. In some cases, the position-time graph can be considered the same as a displacement-time graph. For the following notes, 'positive' and 'negative' refers to direction of velocity rather than magnitude - remember that velocity and acceleration are both vector quantities. 

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Position-time graphs with a straight line (see Fig. 1):

  • the object is moving at a constant speed

  • an upward-pointing line depicts motion being of a positive velocity - in the forwards or upwards direction

  • a downward-pointing line depicts motion being of a negative velocity - in the downwards or backwards direction

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Position-time graphs with a curved line (see Fig. 2):

  • the object is either accelerating in either a positive or negative direction
     

  • if the gradient/velocity is decreasing, the object would be accelerating negatively

    • when the velocity is positive and decreasing, the object is slowing down in the positive direction​

    • when the velocity is negative and decreasing, the object is speeding up in the negative direction
       

  • if the gradient/velocity is increasing, the object would be accelerating positively

    • when the velocity is positive and increasing, the object is speeding up in the positive direction ​

    • when the velocity is negative and increasing, the object is slowing down in the negative direction

Fig. 1 - Position-time graph with a straight line.

Fig. 2 - Position-time graph with a curved line; this graph depicts increasing velocity, therefore positive acceleration.

DISTANCE-TIME GRAPHS​

 

In a distance-time graph, the gradient is the speed. A distance-time graph can never have a negative slope, because distance and speed are both scalar quantities meaning that they do not possess a directional element. The magnitude of speed or distance cannot be below zero. A downwards-sloping line would indicate a decrease in distance, which is not possible - motion in a different direction would still contribute to an increasing amount of length being covered.

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Distance-time graphs with a straight line:

  • the object is moving at a constant speed

  • if the gradient is greater than zero, distance is being covered at the given speed (gradient)

  • if the gradient is zero, distance is not being covered and the object is stationary

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Distance-time graphs with a curved line:

  • the object is either accelerating or decelerating

  • if the gradient is decreasing, the object would be decelerating

  • if the gradient is increasing, the object would be accelerating

VELOCITY-TIME GRAPHS​

 

In a distance-time graph, the gradient is the acceleration; the area under the graph is displacement. The velocity is indicated by the y-axis value, whereas time lies on the x-axis as usual. For the following notes, 'positive' and 'negative' refers to direction of velocity rather than magnitude - remember that velocity and acceleration are both vector quantities. 

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Velocity-time graphs with a straight line:

  • the object is moving at a constant acceleration
     

  • if the gradient is zero, the velocity is constant and the object is not accelerating
     

  • if the gradient is greater than zero, the object is accelerating positively

    • if the gradient is greater than zero and the velocity is negative (y-axis value), the object is slowing down in the negative direction​

    • if the gradient is greater than zero and the velocity is positive (y-axis value), the object is speeding up in the positive direction
       

  • if the gradient is less than zero, the object is accelerating negatively

    • if the gradient is less than zero and the velocity is negative, the object is speeding up in the negative direction​

    • if the gradient is less than zero and the velocity is positive, the object is slowing down in the positive direction

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Velocity-time graphs with a curved line:

  • the object is moving with a non-constant acceleration

  • the same rules as above will apply, keeping in mind that the acceleration (whether positive or negative) is not constant

ACCELERATION-TIME GRAPHS​

 

In an acceleration-time graph, the gradient is the jerk; the area under the graph represents the change in velocity. The jerk is a quantity that describes change in acceleration. The change in velocity is not the same as the initial or final velocity. 

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Acceleration-time graphs with a straight line:

  • if the gradient is zero, the object is moving at a constant acceleration

  • if the gradient is greater or less than zero, the object is moving at a non-constant acceleration
     

Acceleration-time graphs with a curved line:

  • the object is not moving at a constant acceleration

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