Please helpppppp

Question

The height (in centimeters) at time t (in seconds) of a small mass oscillating at the end of a spring is h(t)=8sin(2πt). Estimate its instantaneous velocity at t=6 (Give your answer to four decimal places.)

Velocity at t=6 is approximately

Answer 1

Hi Anjela,

They've given us an equation for position as a function of time. Velocity is the derivative of position (mathematically d/dt p(t) = v(t) where p is a function for position and v is the function for velocity). So let's take a derivative of our height function d/dt h(t)=8sin(2πt) => v(t) = 16π cos(2πt) our velocity function. Now we plug in t=6 to get 50.2655. I hope this helps!

Sincerely, Alexander

Answer 2

For h(t) = 8sin(2πt), the problem is asking for dh/dt. Just need to take the derivative of h(t)

dh/dt = h'(t)= 8(2π)cos(2πt)

h'(6) = 16πcos(12π) = 16π(1) = 16π cm/sec ≈ 50.2655 cm/sec

Note: Starting at 0, 12π is 6 times around the unit circle and back to 0 and cos(0) = 1