A particle moving along the x-axis has acceleration at time , given by , where and are constants. The particle at has zero velocity. In the time interval between and the instant when the velocity () of the particle is then:
Step 1: Given Data
, then we have
Step 2: Formula used
Acceleration is defined the rate of change in velocity :
Step 3: Calculations
The equation of motion of this particle is given as:
Acceleration
The time interval between and the instant when .
We require to find the instant at which.
At , then we have
Since is a constant T.
At the instant the acceleration.
Acceleration,
Thus integrating the above equation within the limits of and , is the velocity of the particle,
Hence, In the time interval between and the instant when the average velocity () of the particle is .