Question
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.
Answers
GPT 3.5
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)
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)