The position (x) of a particle of mass 2 kg moving along x axis at time t is given by x=(2t) m. Find the work done by force actong on it in time interval t=0 to t= 2 s?

Question

Answer

Given

Mass of the particle = 2 kg

Position of the particle along x-axis at time t = x = 2t m

Time interval = t = 0 to t = 2 s

Calculating Velocity and Acceleration

Velocity (v) = dx/dt = 2 m/s

Acceleration (a) = dv/dt = d²x/dt² = 0 m/s²

Calculating Work Done

Work done (W) = Change in Kinetic Energy (KE)

KE = (1/2)mv²

Initial velocity (u) = 0 m/s

Final velocity (v) = 2 m/s

Substituting values

KE = (1/2) x 2 kg x (2 m/s)² = 4 J

Final Answer

The work done by the force acting on the particle in the time interval t = 0 to t = 2 s is 4 J.

Explanation

The given equation x = 2t represents the position of the particle along the x-axis at time t. To calculate the work done by the force acting on the particle, we need to calculate its velocity and acceleration.

Since the derivative of x with respect to t gives the velocity, we get v = dx/dt = 2 m/s. Similarly, the derivative of velocity with respect to time gives acceleration, and we get a = dv/dt = d²x/dt² = 0 m/s².

Now, we can calculate the work done by the force using the formula W = Change in Kinetic Energy (KE). We know that KE = (1/2)mv², where m is the mass of the particle, and v is its velocity. We can calculate the initial velocity to be u = 0 m/s since the particle starts from rest.

Substituting values, we get KE = (1/2) x 2 kg x (2 m/s)² = 4 J. Therefore, the work done by the force acting on the particle in the time interval t = 0 to t = 2 s is 4 J.

Answer

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