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**sderosa518** A particle moves that its position vector r at the time t is given by

r = c ( t - 1/3 t^3) i + ct^2 j

Where c is a positive constant.

Find the velocity at time t(> 0) and show that’s its magnitude increase with time.

Determine its direction of motion at time t=0 show that the directions turns through a right angle between t =0 and t=1.

Show also that the component of force acting on the particle in the direction of the vector j is constant throughout the motion.

Given that c=1, find the maximum displacement of the particle in the I direction and draw a rough sketch of the path of the particle for values of t> 0, showing clearly the positions of the particle at times t=0, 1, radical 3, 2.