Question

A particle moves according to a law of motion $s = f(t)$, $t \ge 0$, where $t$ is measured in seconds and $s$ in feet. $f(t) = 0.01t^4 - 0.05t^3$ (a) Find the velocity at time $t$ (in ft/s). $v(t) = \boxed{\phantom{0.04t^3 - 0.15t^2}}$ (b) What is the velocity after 2 second(s)? $v(2) = \boxed{\phantom{-0.34}}$ ft/s (c) When is the particle at rest? $t = \boxed{\phantom{0}}$ s (smaller value) $t = \boxed{\phantom{3.75}}$ s (larger value)

Name: a particle moves according to a law of motion s ft t ge 0 where t is measured in seconds and s in feet ft 001t4 005t3 a find the velocity at time t in fts vt boxedphantom004t3 015t2 b what i 68055
Uploaded: 2023-03-11T08:50:03-08:00
Duration: 1 min 48 s
Channel: Sri K
Description: a particle moves according to a law of motion s ft t ge 0 where t is measured in seconds and s in feet ft 001t4 005t3 a find the velocity at time t in fts vt boxedphantom004t3 015t2 b what i 68055

          A particle moves according to a law of motion $s = f(t)$, $t \ge 0$, where $t$ is measured in seconds and $s$ in feet.
$f(t) = 0.01t^4 - 0.05t^3$
(a) Find the velocity at time $t$ (in ft/s).
$v(t) = \boxed{\phantom{0.04t^3 - 0.15t^2}}$
(b) What is the velocity after 2 second(s)?
$v(2) = \boxed{\phantom{-0.34}}$ ft/s
(c) When is the particle at rest?
$t = \boxed{\phantom{0}}$ s (smaller value)
$t = \boxed{\phantom{3.75}}$ s (larger value)

a particle moves according to a law of motion s ft t ge 0 where t is measured in seconds and s in feet ft 001t4 005t3 a find the velocity at time t in fts vt boxedphantom004t3 015t2 b what i 68055

Added by Gregorio C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

03/11/2023

Step 1

01t^4 - 0.05t^3$. To find the velocity $v(t)$, we need to take the derivative of the position function with respect to time $t$. $v(t) = f'(t) = \frac{d}{dt}(0.01t^4 - 0.05t^3)$ Using the power rule for differentiation, $\frac{d}{dt}(at^n) = Show more…

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A particle moves according to a law of motion $s = f(t)$, $t \ge 0$, where $t$ is measured in seconds and $s$ in feet. $f(t) = 0.01t^4 - 0.05t^3$ (a) Find the velocity at time $t$ (in ft/s). $v(t) = \boxed{\phantom{0.04t^3 - 0.15t^2}}$ (b) What is the velocity after 2 second(s)? $v(2) = \boxed{\phantom{-0.34}}$ ft/s (c) When is the particle at rest? $t = \boxed{\phantom{0}}$ s (smaller value) $t = \boxed{\phantom{3.75}}$ s (larger value)