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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?
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The position (x) of a particle of mass 2 kg moving along x axis at tim...
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.
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