The equation gives the position $s = f(t)$ of a body moving on a coordinate line (s in meters, t in seconds). Find the body's velocity at time $t = frac{pi}{4}$ sec. $s = 8sin t - cos t$ A. $frac{7sqrt{2}}{2}$ m/sec B. $-frac{9sqrt{2}}{2}$ m/sec C. $frac{9sqrt{2}}{2}$ m/sec D. $-frac{7sqrt{2}}{2}$ m/sec
Added by Benjamin R.
Close
Step 1
This will give us the velocity function. The position function is given by: s(t) = 8\sin(t) - \cos(t) The derivative of the position function with respect to time t is: v(t) = \frac{d}{dt}(8\sin(t) - \cos(t)) Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 94 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Give the position $s=f(t)$ of a body moving on a coordinate line ( $s$ in meters, $t$ in seconds). Find the body's velocity, speed, acceleration, and jerk at time $t=\pi / 4 \mathrm{~s}$. $$ s=\sin t+\cos t $$
Derivatives
Derivatives of Trigonometric Functions
Give the position $s=f(t)$ of a body moving on a coordinate line ( $s$ in meters, $t$ in seconds). Find the body's velocity, speed, acceleration, and jerk at time $t=\pi / 4$ sec. $s=\sin t+\cos t$
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD