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Speed & Velocity (DP IB Physics)

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DP Physics: SLDP Physics: HL

Speed & Velocity

Speed

  • The speed of an object is the distance it travels every second

  • Speed is a scalar quantity

    • This is because it only contains a magnitude (without a direction)

  • The average speed of an object is given by the equation:

a v e r a g e italic space s p e e d space equals space fraction numerator space t o t a l italic space d i s t a n c e over denominator t i m e italic space t a k e n end fraction

  • The SI units for speed are meters per second (m s−1) but speed can often be measured in alternative units e.g. km h−1 or mph, when it is more appropriate for the situation

Velocity

  • The velocity of a moving object is similar to its speed and also describes the direction of the velocity

  • Velocity is defined as:

    The rate of change of displacement

  • Velocity is, therefore, a vector quantity because it describes both magnitude and direction

The difference between speed and velocity

  • Speed is a scalar quantity whilst velocity is vector

    • Velocity is the speed in a given direction

Speed & Velocity, downloadable IGCSE & GCSE Physics revision notes

The cars in the diagram above have the same speed (a scalar quantity) but different velocities (a vector quantity). Fear not, they are in different lanes!

  • This means velocity can also have a negative value

    • E.g. a ball thrown upwards at a velocity of 3 m s–1 comes down at a velocity –5 m s–1, if upwards is considered positive

    • However, their speeds are still 3 m s–1 and 5 m s–1 respectively

Instantaneous Speed & Velocity

  • The instantaneous speed (or velocity) is the speed (or velocity) of an object at any given point in time

  • This could be for an object moving at a constant velocity or accelerating

    • An object at constant velocity is shown by a straight line on a displacement – time graph

    • An object accelerating is shown by a curved line on a displacement – time graph

    • An accelerating object will have a changing velocity

  • To find the instantaneous velocity on a displacement-time graph:

    • Draw a tangent at the required time

    • Calculate the gradient of that tangent

Instantaneous velocity on s-t graph, downloadable AS & A Level Physics revision notes

The instantaneous velocity is found by drawing a tangent on the displacement time graph

  • In the graph above, at t = 9 s, the velocity is:

g r a d i e n t space equals space fraction numerator 10 space minus space 0 over denominator 14 space minus space 5 end fraction space equals space 1.11 space straight m space straight s to the power of negative 1 end exponent

Average Speed & Velocity

  • The average velocity v with bar on top of an object can be calculated using

v with bar on top space equals space fraction numerator increment x over denominator increment t end fraction

  • Where:

    • increment x = total displacement, or change in position (m)

    • increment t = total time taken (s)

  • If the initial velocity u and final velocity v are known, the average velocity can also be calculated from

v with bar on top space equals space fraction numerator open parentheses u space plus space v close parentheses over denominator 2 end fraction

  • To find the average velocity on a displacement-time graph, divide the total displacement (on the y-axis) by the total time (on the x-axis)

    • This method can be used for both a curved or a straight line on a displacement-time graph

Worked Example

Florence Griffith Joyner set the women’s 100 m world record in 1988, with a time of 10.49 s.

Calculate her average speed during the race.

Answer:

  • Sprinters typically speed up from rest to a maximum speed

  • Because Florence’s speed changes over the course of the race, we can calculate her average speed using the equation:

average speed = total distance ÷ time taken

  • Where:

    • Total distance, s = 100 m

    • Time taken, t = 10.49 s

average speed = 100 ÷ 10.49 = 9.5328 = 9.53 m s−1

Worked Example

The variation of displacement of a box sliding across a rough surface with time t is shown on the graph below.

1-1-2-instantaneous-velocity-we-ib-2025-physics

The magnitudes of the instantaneous velocities of the trolley at time t1 and t2 are v1 and v2 respectively. 

List the following velocities in order from fastest to slowest:

v1

v2

average velocity

Answer:

Step 1: Sketch the velocities from the graph

  • The instantaneous velocity is the gradient of a tangent at a certain time

1-1-2-instantaneous-velocity-we-solution-ib-2025-physics

  • The average velocity is the total displacement over the total time

Step 2: Compare the gradients of each velocity

  • The fastest velocity will have the steepest gradient and the slowest velocity the shallowest gradient

  • In order from fastest to slowest:

v1 > average velocity > v2

Examiner Tips and Tricks

When you draw a tangent to a curve, make sure it just touches the point at which you wish to calculate the gradient. The angle between the curve and the tangent line should be roughly equal on both sides of the point.

If you are asked to find the instantaneous velocity from a graph, you will be told the time at which they want this velocity for.

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    Ashika

    Author: Ashika

    Expertise: Physics Project Lead

    Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.