An object moves along the x-axis so that its position at any time t≥0 is given by x(t)=cos(2t2−t+5) . Find the velocity of the object as a function of t.

Answer 1

To find the velocity of the object, we need to take the derivative of the position function with respect to time.

We have x(t) = cos(2t^2 - t + 5)

Taking the derivative, we use the chain rule:

x'(t) = -sin(2t^2 - t + 5) * (4t - 1)

Therefore, the velocity of the object as a function of t is given by:

v(t) = -sin(2t^2 - t + 5) * (4t - 1)