What is the force applied on an object with a mass of 2 kg if the displacement of the object as a function of time is x(t) = 3t^2 - 5t + 18

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justaguide | College Teacher | (Level 2) Distinguished Educator

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Force is given by the product of mass and acceleration. If we have the displacement of an object as a function of time f(t), we can derive the velocity of the object at any moment of time t by calculating the first derivative f'(t). Similarly, the acceleration of the body at moment of time is given by the second derivative f''(t).

Here, the displacement of the object is a function of time, x(t) = 3t^2 - 5t + 18

x'(t) = 6t - 5

x''(t) = 6

This gives the acceleration of the object as constant and equal to 6 unit distance/(unit time)^2

Force is equal to mass*acceleration.

As the mass of the object is 2 kg, the force being applied on it is a constant and is equal to 2*6 kg*unit distance/(unit time)^2

=> 12 kg*unit distance/(unit time)^2

The result has been left in this form as the units of time and length in the function x(t) are not specified.