Motion Along a Line In Exercises 81-84, the function
describes the motion of a particle along a line. (a) Find the velocity function of the particle at any time
. (b) Identify the time interval (s) on which the particle is moving in a positive direction. (c) Identify the time interval(s) on which the particle is moving in a negative direction, (d) Identify the time(s) at which the particle changes direction.
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Calculus of a Single Variable
- The function s(t) describes the motion of a particle along a line. (a) Find the velocity function of the particle at any time t ≥ 0. (b) Identify the time interval(s) on which the particle is moving in a positive direction. (c) Identify the time interval(s) on which the particle is moving in a negative direction. (d) Identify the time(s) at which the particle changes directionarrow_forwardculus I /My courses / MATH1200 / Current Activity / Self Study Activity Semester 2, AY 2021-2022 The position of a hummingbird flying along a straight line in t seconds is given by s(t) = 8t3 15t meters. (a) Determine the velocity of the bird at t = 5 sec. 585 meter/sec on (b) Determine the acceleration of the bird at t = 5 sec. 240 meter/sec² (c) Determine the acceleration of the bird when the velocity equals 0. meter/sec? age Next page here to searcharrow_forwardThe price p (in dollars per pound) and demand a (in pounds) for almonds are related by r = 5600 In(16p²) + 5000. If the current price is $2.25 per pound and is increasing at a rate of $0.20 per week, find the rate of change (in pounds per week) of the supply. (Round off your answer to a whole number) item 3 pdfarrow_forward
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- The rate of disbursement dQ/dt of a $8 million federal grant is proportional to the square of 100 − t, where t is the time (in days, 0 ≤ t ≤ 100) and Q is the amount that remains to be disbursed. Find the amount that remains to be disbursed after 50 days. Assume that the entire grant will be disbursed after 100 days.arrow_forwardThe temperature Tin a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1, 2, 2) is 160°. (a) Find the rate of change of Tat (1, 2, 2) in the direction toward the point (3, 3, 5). (b) Show that at any point in the ball the direction of greatest increase in temperature is given by a vector that points towards the origin.arrow_forwardThe position of a particle as a function of time is shown in the figure. Position (m) What is the particle's average velocity between time t= 0.6s and time t= 7.6 s? (5-34) m/s 76-06 What is the average speed of the particle between time t=0.6s and time te 76 s? 2.317 • What is the average acceleration of the particle in the time interval between t 0.6s and 1= 7/6 s? # Time (s)arrow_forward
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- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage