A particle moving along x- axis has acceleration f at time t given by ...
Acceleration and Velocity of a Particle Moving on x-axis
Given Information:
- Particle moves along x-axis
- Acceleration at time t is given by f = fo[1 t / T], where fo and t are constants
- Particle has zero velocity at t=0
Finding Velocity:
To find the velocity of the particle at the instant when f=0, we need to integrate the acceleration function with respect to time to get the velocity function.
Integration of Acceleration:
Taking the integral of the above acceleration function with respect to time, we get:
Simplifying the above equation, we get:
When f=0:
To find the velocity of the particle when f=0, we need to determine the value of t when f=0.
Solving the above equation, we get:
Therefore, the time interval between t=0 and t=-T is:
Substituting the value of t in the velocity function, we get:
Simplifying the above equation, we get:
Therefore, the velocity of the particle at the instant when f=0 is -fo/2.
Conclusion:
The velocity of the particle at the instant when f=0 is -fo/2.