Kinematics describes the motion of objects without looking at the forces involved in that motion. This post outlines some key definitions and gives some worked examples that should hopefully give you a good understanding of kinematics.
Definitions
Displacement – the distance moved by an object in a given direction.
Displacement is a vector quantity. It has both magnitude (size) and direction. Figure 1 illustrates the difference between distance ( a scalar quantity) and displacement.
As a person walks through the maze the distance they travel is 200m due to the turns they have taken. However, their displacement from the start point to the end point of the maze is only 10m North.
Speed – the distance moved by an object per unit time.
Speed is a scalar quantity. It only has magnitude.
Average Speed – the total distance travelled per unit time.
Average speed can be calculated using the following equation:
Instantaneous Speed – the speed at a given instant in time.
Velocity – the displacement of an object per unit time.
Like displacement, velocity is a vector quantity. Velocity can be calculated using the following equation:
If we know it took the person in Figure 1 10 minutes to get to the end of the maze we can calculate their average speed and velocity:
Note: the velocity states the direction.
Acceleration – the rate of change of velocity.
Acceleration is also a vector quantity (having both magnitude and direction) and can be calculated using the following equation:
In this equation v represents the final velocity of the object and u represents the initial velocity of the object.
Worked Examples
Example 1
A runner starts from rest and reaches a maximum velocity of 3ms-1 in 5s. Calculate the acceleration of the runner to reach this velocity.
Example 2
A car accelerates from rest at a rate of 5ms-2 to a maximum velocity of 23ms-1. Calculate the time the car was accelerating to reach this velocity.
Example 3
A ball travelling at 6ms-1 begins to roll down a hill reaching a velocity of 14ms-1 in 10s. Calculate the acceleration of the ball to reach this velocity.
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