# What is the instantaneous velocity of an object moving in accordance to # f(t)= (sin(2t-pi/2),cost/t ) # at # t=(3pi)/8 #?

We're asked to find the instantaneous velocity of an object, given its position equation.

In component equations, the position is

The velocity can be found by differentiating the position equations:

The magnitude of the instantaneous velocity is thus

And the direction is

By signing up, you agree to our Terms of Service and Privacy Policy

The instantaneous velocity of the object at ( t = \frac{3\pi}{8} ) can be found by taking the derivative of the function ( f(t) ) with respect to ( t ), then evaluating it at ( t = \frac{3\pi}{8} ). Given the function ( f(t) = (\sin(2t-\frac{\pi}{2}), \frac{\cos(t)}{t}) ), the instantaneous velocity can be calculated as follows:

[ f'(t) = \left(2\cos(2t-\frac{\pi}{2}), -\frac{\sin(t)}{t} - \frac{\cos(t)}{t^2}\right) ]

Now, substitute ( t = \frac{3\pi}{8} ) into ( f'(t) ) to find the instantaneous velocity vector at ( t = \frac{3\pi}{8} ).

By signing up, you agree to our Terms of Service and Privacy Policy

- Using the limit definition, how do you find the derivative of # f(x)=4x^2#?
- What is the equation of the tangent line of #f(x) = (4x)/(x-1)# at #x=0#?
- How do you find the equation of the tangent line to the curve #y=x^2+2e^x# at (0,2)?
- How do you find the equation of a line tangent to the function #y=x^2(x-2)^3# at x=1?
- What is the instantaneous velocity of an object with position at time t equal to # f(t)= (1/(t-4),sqrt(5t-3)) # at # t=2 #?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7