Statement 1 If the average velocity and average acceleration...

Statement 1
If the average velocity and average acceleration of a particle in $1-\mathrm{D}$ motion is zero, during certain time interval, it need not be at rest in that duration.
and
Statement 2
The average values do not impose restrictions on the instantaneous values at every point.

Key Concepts

Average Velocity

Average velocity is defined as the total displacement divided by the total time taken. This concept is used to characterize the overall change in position over a given time interval, without providing specific information about how the velocity varies at different instants within the interval.

Average Acceleration

Average acceleration is defined as the change in velocity divided by the time over which that change occurs. Similar to average velocity, this measure gives an overall idea of how the velocity has changed over an interval, but it does not offer details about the instantaneous acceleration at any specific moment.

Instantaneous Values

Instantaneous velocity and instantaneous acceleration represent the values of these quantities at a particular moment in time, given by the derivatives of position and velocity with respect to time, respectively. They can vary significantly throughout the motion, even if the averages over a period appear to be zero.

Relationship between Average and Instantaneous Quantities

The average values of velocity and acceleration provide an overall summary of motion over a period, but they do not constrain or determine the instantaneous values at every point in time. This means that a particle can have non-zero instantaneous velocity or acceleration during an interval even if the average over that interval is zero.

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