A particle moves along a line so that its position at any time t, in seconds, is s(t) = t^3 + 7t^2 + 11t - 2.5. a. Find the velocity and acceleration function at any time t. b. Find the times when the particle is at rest, and the times when it is speeding up and slowing down. Justify your answers. c. Find the values of t when the particle changes direction.

Name: a particle moves along a line so that its position at any time t in seconds is stt37t211t 25 a find the velocity and acceleration function at any time t b find the times when the particle is 18868
Uploaded: 2022-03-31T13:40:09-08:00
Duration: 3 min 36 s
Channel: Chandra Jain
Description: a particle moves along a line so that its position at any time t in seconds is stt37t211t 25 a find the velocity and acceleration function at any time t b find the times when the particle is 18868

          A particle moves along a line so that its position at any time t, in seconds, is s(t) = t^3 + 7t^2 + 11t - 2.5.
a. Find the velocity and acceleration function at any time t.
b. Find the times when the particle is at rest, and the times when it is speeding up and slowing down. Justify your answers.
c. Find the values of t when the particle changes direction.

Added by Brian W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Chandra Jain

03/31/2022

Step 1

\[ s(t) = t^3 + 7t^2 + 11t - 2.5 \] \[ v(t) = \frac{d}{dt} s(t) = \frac{d}{dt} (t^3 + 7t^2 + 11t - 2.5) \] \[ v(t) = 3t^2 + 14t + 11 \] Show more…

Show all steps

Thanks for your feedback!

A particle moves along a line so that its position at any time t, in seconds, is s(t) = t^3 + 7t^2 + 11t - 2.5. a. Find the velocity and acceleration function at any time t. b. Find the times when the particle is at rest, and the times when it is speeding up and slowing down. Justify your answers. c. Find the values of t when the particle changes direction.