A particle moves along the x-axis. Its position varies with time according to x(t)...

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Step by step solution to the problem:
"A 4.20 kg particle moves along the x-axis. Its position varies with time according to x(t) = t + 3.0t^3, where x is in meters and t in seconds:
a) Find the kinetic energy of the particle at any time t
b) Find the magnitude of the acceleration and the force acting on the particle at any time t
c) Find the power being delivered to the particle at any time t
d) Find the work done in the particle in the interval t = 0 to t = 1.5 seconds

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Step by step solution:a)Considering() = + 3.0 3We can calculate the formula for the speed as:() =()= 1 + 9.0 2Thus, considering the equation for the kinetic energy is:=12 (())2Substituting m = 4.20 kg and the expression we have found for V(t),=11 4.2 (1 + 9.0 2 )2 = 4.2 (1 + 18. 0 2 + 81.0 4 )22Operating, = 2.1 + 37.8 2 + 170.1 4b)Considering() = + 3.0 3We can calculate the formula for the acceleration as:() =2 ()= 18.0 2On the other hand, we can calculate the force F by applying the law of Newton: =Substituting the equation we just found for a(t):() = 4.20 18.0 = 75.6 c)Since =
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