FHSST Physics/Rectilinear Motion/Speed and Velocity

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The Free High School Science Texts: A Textbook for High School Students Studying Physics
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Rectilinear Motion
Definition - Speed and Velocity - Graphs - Equations of Motion - Important Equations and Quantities

Speed and Velocity[edit]

Let's take a moment to review our definitions of velocity and speed by looking at the worked example below:

Worked Example 23 Speed and Velocity[edit]

Fhsst rectmot2.png

Question: A cyclist moves from A through B to C in 10 seconds. Calculate both his speed and his velocity.

Answer:

Step 1 :

Analyse the question to determine what is given. The question explicitly gives

  • the distance between A and B
  • the distance between B and C
  • the total time for the cyclist to go from A through B to C

all in the correct units!

Step 2 :

What is being asked? We are asked to calculate the average speed and the average velocity of the cyclist.

His speed - a scalar - will be

Since velocity is a vector we will first need to find the resultant displacement of the cyclist. His velocity will be


The total displacement is the vector from A to C, and this is just the resultant of the two displacement vectors, i.e.

Using the rule of Pythagoras:


For this cyclist, his velocity is not the same as his speed because there has been a change in the direction of his motion. If the cyclist traveled directly from A to C without passing through B his speed would be

and his velocity would be

In this case where the cyclist is not undergoing any change of direction (i.e. he is traveling in a straight line) the magnitudes of the speed and the velocity are the same. This is the defining principle of rectilinear motion.

Important:
For motion along a straight line the magnitudes of speed and velocity are the same, and the magnitudes of the distance and displacement are the same.