Put simply:
- A scalar quantity is represented by a numerical value only. It is generally representative of the total distance traveled, speeds etc and the direction of these quantities are not needed.
- A vector quantity is represented by a numerical value and a direction. It is not concerned with the total distance traveled or changing speeds, merely the shortest straight line value between point A and point B
Distance and Displacement, can these help explain these?
Lets start out with distance. Distance is the scalar quantity that says, "how far in total did an object move?" An odometer in a car is a good example of something that measures distance. This is because it is not concerned with
the direction of the travel, only the amount of road covered.
Displacement however, refers to how far away in a straight line has an object moved from its starting point.
Using the above example the distance a person has moved is 50 paces.
The persons displacement (shown by the red arrow) is approximately 36 paces in a NE direction. A little knowledge of Pythagoras will go a long way.
Lets start out with distance. Distance is the scalar quantity that says, "how far in total did an object move?" An odometer in a car is a good example of something that measures distance. This is because it is not concerned with
the direction of the travel, only the amount of road covered.
Displacement however, refers to how far away in a straight line has an object moved from its starting point.
Using the above example the distance a person has moved is 50 paces.
The persons displacement (shown by the red arrow) is approximately 36 paces in a NE direction. A little knowledge of Pythagoras will go a long way.
What's the difference between scalars and vectors?
Speed is a scalar quantity that explains how fast an object moves or at what rate it travels a measured distance. Hence
Velocity is a vector quantity which describes the rate at which an object changes position from its start position to its finishing point. Therefore
eNOTE: Because displacement notes the direction, velocity must do so as well.
Lets go back to this example and say that the person took 50 seconds to complete their journey. The speed is 50 paces / 50 seconds, and so is
1 pace/second.
The velocity is 36 paces NE / 50 seconds, so the velocity is (approximately)
0.7 paces/second NE.
Instantaneous speed/velocity and average speed/velocity.
Instantaneous speed/velocity is the speed/velocity at any instant. It can be measured using a speed gun or a speedometer.
Average speed/velocity is the average of all instantaneous speed over a journey. This quantity is calculate using the formula above.
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