Lesson 1: Vector and Scalar Quantities
Understanding Vector and Scalar Quantities
Scalar quantities are quantities that have only magnitude. Now, what's magnitude? Magnitude is just a number with units. So, can you think of an example of a scalar quantity? Yeah, miles per hour, like I can say 40 miles per hour. We have a number and we have our units. Now a vector quantity does have magnitude but it also has direction. Instead of saying 40 miles per hour, I would say 40 miles per hour north because you have your magnitude and you have a direction. Now a direction doesn't have to be north, it can be northeast, southwest, left, right, forward, backward.
One type of scalar quantity is distance. Distance with direction is called displacement. Now we all know what distance is, right? Say this is your home and point B is the supermarket. So your road takes you here, here, here, here, here, and then finally you're at your supermarket. So the distance it takes to get from point A to point B, that's your distance. And we all know the distance formula: the change in x squared plus the change in y squared, right? But this is our distance. What if we want to find the displacement? Displacement is the shortest distance from point A to point B, so on this route it would be this straight line from A to B.
Example Problems
Example problem:
A car travels along a straight road. It starts from point A and moves to point B, which is 100 m to the east. Then it continues from point B to point C, which is 150 m to the west. What is the displacement?
Solution:
Displacement = Final position - Initial position
= (100 m east - 150 m west)
= -50 m (or 50 m west)
Another example:
What is the difference between distance and displacement if a person walks 3 km north and then 4 km east?
Solution:
Distance = Total path covered
= 3 km + 4 km
= 7 km
Displacement = Shortest distance from the initial to the final position
= sqrt((3 km)^2 + (4 km)^2)
= sqrt(9 + 16)
= sqrt(25)
= 5 km