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The formula for velocity is given by:
v = d/t
where:
- v = velocity (m/s)
- d = distance traveled (m)
- t = time taken (s)
This formula is derived from the basic definition of velocity, which is the rate at which an object changes its position in a given time. Velocity is a vector quantity, which means it has both magnitude and direction.
To derive the formula, consider an object moving in a straight line with a constant velocity v. Let the distance traveled by the object in time t be d. Then, the average velocity of the object during this time period can be given as:
average velocity = distance traveled / time taken v_avg = d/t
However, if the object is moving with a constant velocity, then the average velocity is equal to the instantaneous velocity, which is the velocity of the object at any given moment in time. Therefore, we can rewrite the above equation as:
v = d/t
This formula tells us that the velocity of an object is directly proportional to the distance traveled and inversely proportional to the time taken to cover that distance. In other words, if the distance traveled by an object increases while the time taken to cover that distance remains constant, the velocity of the object will increase. Similarly, if the time taken to cover a certain distance increases while the distance traveled remains constant, the velocity of the object will decrease.