Katy covers basic physics principles in an easy to understand format with insights in how to apply them in the real world.
Speed vs Velocity
The difference between speed and velocity: velocity has a direction and speed does not.
In more precise physics terms:
Velocity is a vector (i.e. includes a direction) and speed is a scalar (i.e. just a number). You can find speed by taking the magnitude of the velocity vector.
Let's look at both elements in more detail and show you some examples.
Speed in Physics
In every day life we know speed as a measure of how fast an object is moving. A car can be fast or slow.
In physics and engineering it has a very specific role: the magnitude of velocity. Speed is the rate at which an object’s position is changing, regardless of the direction it is moving.
Speed is a scalar quantity, meaning it is a number only with no direction specified.
You'll rarely find speed as an input to a physics equation, except in some 1D cases. This is because physical laws act in our real 3D world so equations need a direction specified. Find out more about that in the next section on Velocity.
Velocity in Physics
Velocity is definitely a more complex concept. In conversations we often use speed and velocity interchangeably but they don't mean the same thing.
Velocity is a vector, which means it has a direction component. The direction can be North, South East or West or be described in a coordinate system like x and y.
So instead of just the distance covered in a time span it is the distance in a specific direction. That means velocity will take into account the direction and how much ground is covered.
How to Calculate Speed
Find speed by taking the distance covered divided by the time it took to cover it. See the speed equation in the image above.
Find Distance Traveled
Depending on how the problem is setup you may need to calculate the distance first if it's not given to you.
The units will be distance over time like meters per second or miles per hour.
Read on for worked examples of calculating speed.
How to Calculate Velocity
Find velocity by taking the displacement and dividing it by the time elapsed.
The displacement element in velocity is where the direction is incorporated. Displacement is the change in position from the beginning to end, regardless of how much distance was traveled to get there. Find it by taking the ending position and subtract the starting position.
The units are the same: distance over time. The direction will be spelled out in the answer also.
See worked out examples below.
Example Problem 1: Speed
You drove 50 miles in 2 hours, what was your speed?
We can find this by taking the distance (50 miles) divided by the time (2 hours). 50 divided by 2 is 25. The units will be miles per hour so the answer is 25 mph.
Notice that the question doesn't specify a direction. For a speed calculation it doesn't matter what direction you were driving. If the question had asked you to find velocity you would need more information.
Example Problem #2: Zero Velocity
A runner runs a race on a track that is 400 m in circumference. He starts and ends at the same point and it takes him 40 seconds to complete the race. What is his speed? What is his velocity?
To find his speed, take the distance traveled (400 m) divided by the time elapsed (40 s). 400 divided by 40 is 10. So his speed was 10 m/s.
To find the runner's velocity, take the displacement (0 m) divided by the time elapsed (40 s). 0 divided by 40 is 0. So his velocity was 0 m/s.
Obviously speed and velocity can be very different! this problem shows that understanding the difference between total distance traveled and displacement is important. Since the runner started and stopped at the same point, his displacement was zero. Thus, his velocity was zero.
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