If an object is moving along a straight line and with respect to some reference point, its position is x1 at time t1 and becomes x2 at time t2 . The average velocity of the object during this time interval would be: 

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  1. (x2 / t2 ) + (x1 / t1)
  2. (x2 − x1 ) / t2
  3. x2 / (t2 − t1
  4. (x2 − x1 ) / (t2 − t1

Answer (Detailed Solution Below)

Option 4 : (x2 − x1 ) / (t2 − t1
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Detailed Solution

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The correct answer is (x2 - x1 ) / (t2 - t1 ).

Key Points

  • The average velocity is defined as the total displacement divided by the total time taken.
  • Mathematically, it is expressed as (x2 - x1) / (t2 - t1), where x1 and x2 are the initial and final positions, and t1 and t2 are the initial and final times respectively.
  • This formula provides a measure of how fast an object is moving along a straight line over a specified time interval.
  • Average velocity is a vector quantity, meaning it has both magnitude and direction.
  • It differs from instantaneous velocity, which refers to the speed of an object at a particular moment in time.

Additional Information

  • Displacement
    • It is the shortest distance between the initial and final positions of an object.
    • Displacement is a vector quantity, having both magnitude and direction.
    • It can be zero even if the distance traveled is non-zero, if the object returns to its starting point.
  • Instantaneous Velocity
    • It refers to the velocity of an object at a particular instant of time.
    • Instantaneous velocity can be determined using differential calculus, by taking the derivative of the position function with respect to time.
    • Unlike average velocity, it provides the speed and direction of an object at a specific moment.
  • Speed vs. Velocity
    • Speed is a scalar quantity that refers only to how fast an object is moving.
    • Velocity is a vector quantity that describes both the speed and direction of an object's movement.
    • Average speed is the total distance traveled divided by the total time taken, while average velocity is the total displacement divided by the total time taken.
  • Uniform and Non-Uniform Motion
    • In uniform motion, an object travels equal distances in equal intervals of time.
    • In non-uniform motion, an object travels unequal distances in equal intervals of time.
    • For non-uniform motion, average velocity can provide an overall description of the motion over a time interval.
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