Assume that the force: F= 2x(x+z)i-2(y=z)j=2(x-y)k,N Acting on a particle of mas

Question

Assume that the force:

F= 2x(x+z)i-2(y=z)j=2(x-y)k,N

Acting on a particle of mass M = 0.50 kg. At t = 0 the particle position vector is:

r=3i+2j,m

and has a speed:

v=3j=+8k,m/s

Determine at t = 0:

The force acting on the particle.

The acceleration of the particle

The kinetic energy of the particle

The rate of change of kinetic energy

Now suppose you want to calculate the kinetic energy of the particle at time t = 0.01 s

What is the procedure to calculate the kinetic energy in question?

What is the value of that energy?

Explanation / Answer

F = 18 i -4j +2k a = 36i - 8j +4k Kinetic energy = 0.5*0.5*(9+64) = 18.25J rate of change of kinetic energy = m*V*a = 0.5*(-24+32) = 4J/s if we want to calculate at t=0.001s, we have to calculate the velocity at tat time and acceleration at that time.

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