force acting on a body varies with time as shown below if initial momentum of body is p then time taken by body to retain its momentum p again is
I don't see anything "as shown below"
To determine the time taken by a body to retain its initial momentum, we need to consider the given function showing how the force acting on the body varies with time. However, you haven't provided any specific function or graph to refer to.
In general, when the force acting on a body changes with time, we can use Newton's second law of motion to relate force, mass, and acceleration. The equation is given by:
F = m * a
Where:
- F represents the force acting on the body,
- m represents the mass of the body, and
- a represents the acceleration of the body.
To find the time taken by the body to retain its momentum p again, we can follow these steps:
1. Calculate the initial acceleration (a) using Newton's second law of motion, by dividing the initial force acting on the body by its mass (a = F / m).
2. Integrate the acceleration function with respect to time to obtain the velocity function of the body over time (v = ∫ a dt), where v is the velocity of the body.
3. Integrate the velocity function with respect to time again to get the displacement function of the body over time (s = ∫ v dt), where s is the displacement of the body.
4. Calculate the time taken for the displacement to return to zero or to reach its initial value p, which will give you the time taken for the body to retain its momentum p again.
Please provide the specific function or graph describing how the force acting on the body varies with time so that we can give you a more accurate answer.