Question

A varying force is applied on a body of unit mass and if the force increase the rate of 2N/sec. Then find the rate at which the acceleration in the body is changing.

Answer 1

To find the rate at which the acceleration in the body is changing, we can differentiate the force with respect to time using Newton's second law of motion.

Step-by-step explanation:

To find the rate at which the acceleration in the body is changing, we need to differentiate the force with respect to time. Since the force is increasing at a rate of 2 N/sec, the rate of change of force with respect to time is 2 N/sec. Now, using Newton's second law of motion, which states that force is equal to mass times acceleration (F = ma), we can differentiate this equation with respect to time to find the rate at which acceleration is changing.

dF/dt = m * d/dt(a)

Since the mass of the body is given to be 1 kg (unit mass), and the rate of change of force (dF/dt) is 2 N/sec, we can substitute these values into the equation. Since the mass is constant, we have:

2 N/sec = 1 kg * d/dt(a)

Simplifying, we find d/dt(a) = 2 m/s^2/sec. Therefore, the rate at which the acceleration in the body is changing is 2 m/s^2/sec.

Answer 2

The rate at which the acceleration of a body with unit mass is changing, when the force applied to it increases at a rate of 2 N/sec, is 2 m/s²/sec.

Step-by-step explanation:

The student's question relates to the rate at which acceleration changes when a force is applied to a body of unit mass.

The force is increasing at a constant rate of 2 N/sec.

According to Newton's second law of motion, which defines the relationship between force, mass, and acceleration as F = ma, the acceleration (a) of a body is directly proportional to the net force (F) acting on it and inversely proportional to its mass (m).

Since the mass is given as unit mass (1 kg), the acceleration is equal to the force applied.

Therefore, if the force increases at a rate of 2N/sec, the rate of change of acceleration will also be 2 m/s2/sec because the mass is 1 kg (2 N/kg = 2 m/s2).

Thus, the rate at which the acceleration in the body is changing is 2 m/s2/sec.