What are scalars and vectors? Give examples. How are vectors represented symbolically and graphically?

Scalars are physical quantities that are described by only their magnitude. They do not have a direction. Examples include:

    • Speed: The rate at which an object covers distance (e.g., 60 km/h).
    • Temperature: A measure of the heat or cold of a substance (e.g., 30°C).
    • Mass: The amount of matter in an object (e.g., 5 kg).

  • Vectors are physical quantities that have both magnitude and direction. Examples include:

    • Velocity: The rate at which an object changes its position, with direction (e.g., 60 km/h to the north).
    • Force: A push or pull on an object, which has both magnitude and direction (e.g., 10 N to the right).
    • Displacement: The change in position of an object in a particular direction (e.g., 5 meters to the east).

  • Vector Representation:

    • Symbolically: Vectors are often represented by boldface letters or letters with an arrow on top, such as v for velocity or F for force.
    • Graphically: Vectors are represented by arrows. The length of the arrow represents the magnitude of the vector, and the direction of the arrow shows the direction of th

Related Questions:

  1. Differentiate between rest and motion. With the help of an example, show that rest and motion are relative to an observer.
  2. What are different types of motion? Define each type of motion with examples from daily life.
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  4. In a park, children are enjoying a ride on a Ferris wheel as shown. What kind of motion does the big wheel have, and what kind of motion do the riders have?
  5. A boy moves for some time, give two situations in which his displacement is zero but the distance covered is not zero.
  6. A stone tied to a string is whirling in a circle. What is the direction of its velocity at any instant?
  7. Is it possible to accelerate an object without speeding it up or slowing it down?
  8. Can a car moving towards the right have the direction of acceleration towards the left?
  9. With the help of daily life examples, describe the situations in which: a. Acceleration is in the direction of motion. b. Acceleration is against the direction of motion. c. Acceleration is zero and the body is in motion.
  10. Examine the distance-time graph of a motorcyclist (as shown). What does this graph tell us about the speed of the motorcyclist? Also, plot its velocity-time graph.
  11. Which controls in the car can produce acceleration or deceleration in it?
  12. If two stones of 10 kg and 1 kg are dropped from a 1 km high tower, which will hit the ground with greater velocity? Which will hit the ground first? (Neglect air resistance)
  13. A 100 g ball is just released (from rest) and another is thrown downward with a velocity of 10 m/s. Which will have greater acceleration? (Neglect air resistance)
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