FHSST Physics/Rectilinear Motion/Speed and Velocity

Speed and Velocity 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 263px| 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.