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

Asked on by lxsptter

1 Answer | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

We’ve answered 319,816 questions. We can answer yours, too.

Ask a question