Consider a stock car, which starts from rest at time t=0 with velocity in m/s increasing for 9.5 s according to the function vx = (1.4) t2 + (1.1) t Find the car's velocity at the end of the 9.5 s interval. Give your answer in m/s.
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Consider a stock car, which starts from rest at time t=0 with velocity in m/s increasing for 9.5 s according to the function
vx = (1.4) t2 + (1.1) t
Find the car's velocity at the end of the 9.5 s interval. Give your answer in m/s.
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- A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. f(t) = 0.01t4 − 0.03t3 (a) Find the velocity at time t (in ft/s).v(t) = (b) What is the velocity after 1 second(s)?v(1) = ft/s(c) When is the particle at rest? t = s (smaller value) t = s (larger value) (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) (e) Find the total distance traveled during the first 11 seconds. (Round your answer to two decimal places.) ft(f) Find the acceleration at time t (in ft/s2). a(t) = Find the acceleration after 1 second(s). a(1) = ft/s2 (g) Graph the position, velocity, and acceleration functions for the first 11 seconds. (h) When, for 0 ≤ t < ∞, is the particle speeding up? (Enter your answer using interval notation.) When, for 0 ≤ t < ∞, is it slowing down? (Enter your answer using interval notation.)A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. f(t) = t3 − 15t2 + 72t (a) Find the velocity at time t. v(t) = (b) What is the velocity after 5 s? v(5) = ft/s (c) When is the particle at rest? t = s (smaller value) t = s (larger value) (d) When is the particle moving in the positive direction? (Enter your answer in interval notation.) t (e) Find the total distance traveled during the first 8 s.ft(f) Find the acceleration at time t. a(t) = Find the acceleration after 5 s. a(5) = ft/s2 (g) Graph the position, velocity, and acceleration functions for the first 8 s. (h) When, for 0 ≤ t < ∞, is the particle speeding up? (Enter your answer in interval notation.) When, for 0 ≤ t < ∞, is it slowing down? (Enter your answer in interval notation.)An unidentified flying object (UFO) is observed to travel a total distance of 49000 m, starting and ending at rest, over a duration of 3.07 s. Assuming the UFO accelerated at a constant rate to the midpoint of its journey and then decelerated at a constant rate the rest of the way, what was the magnitude of its acceleration? Express your answer in g s , where 1 g = 9.81 m/s^2. 20,796 g s 10,398 g s 2,120 g s 1,060 g s
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- A spacecraft starts from rest, and makes a journey to a destination 447000 km from its starting point. It does so by accelerating at a constant rate of 9.82 m/s^2 up to the midpoint of the journey, and then decelerates at the same constant rate of 9.82 m/s^2 for the second half of the journey, ending at rest. How long did the entire journey take?The velocity of a partcile is given by the equation v = 5.0 t - 0.60 t2 (in m/s). At t=0, the particle is at rest. At what time will the particle be at rest again?A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. f(t) = 0.01t4 − 0.02t3 a) When, for 0 ≤ t < ∞, is the particle speeding up? (Enter your answer using interval notation.) b) When, for 0 ≤ t < ∞, is it slowing down? (Enter your answer using interval notation.)