Vector and Scalar

Vector and Scalar

  • Vector is a quantity that contains both magnitude and direction
  • Scalar is a quantity that contains magnitude only
  • The magnitude describes the size of a quantity 

For example, a ball travels at 3 meters per second in the left direction.

  • 3 meters per second = magnitude of the quantity = speed
  • left direction = direction 
  • 3 meters per second to the left = velocity

In the unit, we will study

  • Scalar quantities: distance, speed, instantaneous speed
  • Vector quantities: displacement, velocity, acceleration.

Source: http://thescienceclassroom.org/physics/motion-in-1-d/distance-and-displacement/

Displacement and Distance

Displacement

  • A vector quantity
  • Describes an object's change in position.
  • It is equal to final position minus initial position

Distance

  • A scalar quantity
  • Distance refers to the total movement of an object without any regard to direction

Speed and Velocity

Speed

  • A scalar quantity
  • Average speed is equal to total distance travelled divided by the total time, represented by the blue line in the above image. 

Velocity

  • A vector quantity
  • Change in velocity is equal to the difference between an object's final velocity and initial velocity
  • Average velocity is equal to displacement divided by time

Calculating Displacement, Distance, Velocity, and Speed

Example 1: Pythagorean theorem 

A girl run to the left for 3 meters, and then goes up for 4 meters. What is the total displacement the girl travelled? What is the total displace the girl travelled?

  1. To solve the problem, you can sketch a diagram and connect initial and final positions to calculate the displacement. The displacement is equal to the green line. 
  2. Using the Pythagorean theorem, we obtain an answer of 5 meters for displacement.
  3. The distance is equal to the length of total path travelled, which is equal to 4+5=9 meters.

Example 2: Pythagorean theorem 

A person runs to the left at 3m/s for 10 seconds, then he turns his direction and runs to the northern direction at 4m/s for 15 seconds.

  • What is the total displacement and distance?
  • What is the average velocity and average distance?

Vector and Scalar Quiz


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