What is the difference between velocity and speed? Velocity is the vector equivalent of speed. Since speed is the distance travelled per unit time, this means that velocity is displacement travelled per unit time.
If you're estimating how long a journey will take, you will probably use an average velocity. However, sometimes instantaneous velocity is more important.
Key Concepts
Velocity is defined as the rate of change of displacement:
\(v={\Delta s \over \Delta t}\)
The derived SI unit of velocity is m s-1.
Speed is defined as the rate of change of distance:
\(\text {speed} = {\text {distance} \over \text {time}}\)
Speed is a scalar and velocity is a vector. This means if you tavel in a complete circle at constant speed your velocity is constantly changing and your average velocity will be zero.
Watch this clip and notice the changing direction of the velocity arrow.
Any moving object has an instantaneous velocity.
Instantaneous velocity is the velocity you would calculate if you divided motion into small steps and calculated the step length divided by time taken: \(v_{\textrm {instantaneous}}={\delta s \over \delta t}\).
The direction of the velocity is the same as the direction of the change in displacement.
If velocity is constant then average velocity = instantaneous velocity. If velocity is not constant they will be different, average velocity is simply the total displacement / total time. On a graph, these would be found from the final and intial points, ignoring whatever happens between.
Use quizzes to practise application of theory.
START QUIZ!
A car travels at a constant speed of 30 ms-1 for 20s.
Which of the following statements are false
If the velocity is constant then the motion is in a straight line but not necessary if speed is constant.
If the car moves in a curved path then the displacement will be less than 600 m
A car travels for 10s with constant velocity for a distance of 100 m.
Which of the following statements is false:
Constant velocity is the same as constant speed in a fixed direction
Watch the animated dot.
If the length scale is in meters, the magnitude of the average velocity is.
Displacement = 5 m since the horizontal and vertical motion forms a 345 triangle.
Watch the animated dot.
If the length scale is in meters, the average speed is approximately.
The distance travelled is approximately 20 m and the time 5 s. Easier to simply eliminate the other answers as too big or too small.
Observe the motion of the blue dot and answer the questions
The displacement at time 0 s = m
The displacement at time 2 s = m
The total displacement from 0 s to 2 s = m
The velocity of the dot = ms-1
The initial instantaneous velocity of the dot = ms-1
The instantaneous velocity at time 2 s = ms-1
Although the displacement at 2s is 3m the displacement from the original position = 4m so v = 4/2
Another blue dot
The displacement at time 0 s = m
The displacement at time 4 s = m
The total in displacement from 0 s to 4 s = m
The velocity of the dot = ms-1
The initial instantaneous velocity of the dot = ms-1
The instantaneous velocity at time 2 s = ms-1
Displacement is negative so velocity is negative, this is also the direction of motion.
How much of Velocity and speed have you understood?
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