Find the displacement function given that a(t) = 3t^2, v(2) = 9, and s(2) = 12.
Added by James P.
Close
Step 1
First, we know that acceleration is the second derivative of displacement, so we can integrate it twice to find the displacement function: a(t) = 3t^2 Integrating once: v(t) = ∫a(t)dt = t^3 + C1 Integrating again: s(t) = ∫v(t)dt = (1/4)t^4 + C1t + C2 Show more…
Show all steps
Your feedback will help us improve your experience
Sam Stansfield and 69 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
The displacement of a particle is given by x(t) = 4t² + 8t + 2, where length is in meters and time is in seconds. Find the displacement of the particle at t = 2s.
Ivan K.
Find the velocity and acceleration functions for the given position function. $$\mathbf{r}(t)=\langle 2 \cos t+\sin 2 t, 2 \sin t+\cos 2 t\rangle$$
Vector-Valued Functions
Motion in Space
Use the given position function to find the velocity and acceleration functions. $$ s(t)=-4.9 t^{2}+12 t-3 $$
Differentiation
Computation of Derivatives: The Power Rule
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Watch the video solution with this free unlock.
EMAIL
PASSWORD