Question:

3. [-/5 Points] DETAILS SCALCET9 3.XP.7.003. A particle moves according to a law of motion s = f(t), t 2 0, where t is measured in seconds and s in feet. f(t) = te-t/2 (a) Find the velocity at time t (in ft/s). v ( t ) = (b) What is the velocity (in ft/s) after 1 s? (Round your answer to two decimal places.) V(1) = ft/s (c) When (in seconds) is the particle at rest? t = (d) When (in seconds) is the particle moving in the positive direction? (Enter your answer using interval notation.) (e) Find the total distance (in feet) traveled during the first 6 s. (Round your answer to two decimal places.) ft (f) Find the acceleration at time t (in ft/s2). a(t) = Find the acceleration (in ft/s2) after 1 s. (Round your answer to three decimal places.) a(1) = ft/s2 (g) Graph the position, velocity, and acceleration functions for the first 6 s. 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5 a 1 -0.5 v 3 6 7 -0.5 1 3 5 6 7 O-1.0 1 0-1.0 2.0/ y 2.0 1.5 1.5 1.0 1.0 0.5 0.5 -0.5 s 1 -0.5 a 1 3 5 6 7 O-1.0 1 0-1.0 (h) When, for 0 S t