   Question Answers

# The rate of change of displacement with time is (A). Speed(B). Acceleration(C). Retardation(D). Velocity  - Hint: Understand the meaning of the question, i.e. this quantity refers to how fast an object is moving. Remember that fast is a word associated with time.

Formula used: The formula from the definition of velocity is used, which is
$\text{Velocity}=\dfrac{\text{Change in displacement}}{\text{time}}$

Complete step-by-step solution -

Position, displacement, velocity, acceleration and some other physical quantities let us determine motion of an object. Displacement of an object is defined as the difference in the final position from the initial position of an object. For example, consider a motion in one-dimension, if a person P is standing initially at A ($x=1m$ ) and finally moves to point B ($x\text{ }=\text{ 5}m$), where the reference point is O ($x\text{ }=\text{ 0}m$). The displacement for this journey will be $4m$. Refer to the figure.

For the example that was considered above, let the time taken to complete the journey be T. The rate of displacement with respect to time essentially means how fast the person or the object has travelled from initial position A in order to reach the final location B in the given time interval T.
Velocity is defined as the rate of displacement with respect to time. Assuming the person moved in a uniform motion, the answer to how fast he/she travelled is the velocity. The formula for velocity is
$\text{Velocity}=\dfrac{\text{Change in displacement}}{\text{time}}$
Therefore, the answer to this question is D. Velocity.

Note: Do not get confused between speed and velocity. Speed is the magnitude of velocity. This means that velocity gives a sense of direction for the motion, whereas speed gives only its magnitude.
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