Linear Kinematics : Velocity & Acceleration

Speed Displacement - the change in position in a particular direction and is always a straight line segment from one point to another. Displacements are vector quantities and can be combined in vector fashion. Motion – the displacement of an object in relation to objects that are considered to be stationary. The rate of motion is called speed

e.g. you are riding a bike at 6 m/s You travel 6 m in 1 second, 12 m in 2 seconds.

Slope A = 3/1 = 3 m/s Slope B = 3/3 = 1 m/s Slope C =1/3 = 0.33 m/s Speed can be graphed with a displacement vs. time graph. This graph shows three lines of constant speed. In other words, the speed remained the same over the entire displacement and the result is a straight line graph.

The average speed is found by dividing the total distance by the elapsed time. In most cases objects do not move with a constant speed. Initially and at the end, the speed is likely to be less. Suppose you ride your bike 120m in 20s. Your average speed is = 6m/s A graph of your speed might look like fig 3-3 You start at 0.0 m/s, increase to a constant speed between 3 and 15 s then begin to slow down.

Instantaneous speed is the slope of the line at a point in the line. This would be shown by the slope of the line that is tangent to the speed curve. Without calculus, the only way to measure instantaneous speed is to calculate the slope of a tiny portion of the speed curve.

On our graph, the initial speed A is approx. 3.9 m/s, the constant speed B is approx. 7.5 m/s, and the final speed C is approx. 4.5 m/s. Speed is a scalar quantity, meaning that no direction is implied. It is

Velocity is speed in a particular direction. When you are given the speed of the object and the direction it is headed, you know the velocity. This makes it a vector quantity. Remember velocity may be positive (+ve) or negative (-ve) to indicate some direction. Velocity

Recall that ∆ is the Greek symbol delta and means “change in”

In this graph, (fig 3- 4) the velocity over the entire range is constant Similarly, the velocity between points A and B on the graph is The motion of this object is said to be uniform (i.e. it doesn't change through the graph).

A graph with variable motion is shown in fig 3-5. The average velocity is The velocity between points C & D is

The velocity at the specific point C is found by drawing the tangent and finding its slope. The velocity at a specific instant in variable motion is also called instantaneous velocity.