Question

#3. A particle moves in a straight line such that its displacement, x meters, from a fixed point O on the line at time t seconds is given by x(t) = (t - 2)$^3$ - 3t + 8. (a) [2 points] Find the time when the particle is instantaneously at rest. (b) [1 point] Find the displacement of the particle from O when t = 4 s. (c) [3 points] Find the total distance traveled during the first 4 seconds of its motion.

          #3. A particle moves in a straight line such that its displacement, x meters, from a fixed point O on the line at time t seconds is given by x(t) = (t - 2)$^3$ - 3t + 8.
(a) [2 points] Find the time when the particle is instantaneously at rest.
(b) [1 point] Find the displacement of the particle from O when t = 4 s.
(c) [3 points] Find the total distance traveled during the first 4 seconds of its motion.

#3. A particle moves in a straight line such that its displacement, x meters, from a fixed point O on the line at time t seconds is given by x(t) = (t - 2)^3 - 3t + 8.
(a) [2 points] Find the time when the particle is instantaneously at rest.
(b) [1 point] Find the displacement of the particle from O when t = 4 s.
(c) [3 points] Find the total distance traveled during the first 4 seconds of its motion.

Added by Kathleen V.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/22/2023

Step 1

Velocity is the derivative of displacement with respect to time, so we need to find the derivative of x(t) with respect to t. Show more…

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#3. A particle moves in a straight line such that its displacement, x meters, from a fixed point O on the line at time t seconds is given by x(t) = (t-2)^(3) - 3t + 8. (a) [2 points] Find the time when the particle is instantaneously at rest. (b) [1 point] Find the displacement of the particle from O when t = 4s. (c) [3 points] Find the total distance traveled during the first 4 seconds of its motion.