89. A particle moves on a vertical line so that its coordinate a time t is y = t – 12t + 3, t> 0. (a) Find the velocity and acceleration functions. (b) When is the particle moving upward and when is it moving downward? (c) Find the distance that the particle travels in the time interval 0 < t < 3. (d) Graph the position, velocity, and acceleration function for 0 < t< 3. (e) When is the particle speeding up? When is it slowing down2

Q: The graph of the velocity function v = v(t) is given below. Determine the distance trav- eled during…

A: Distance traveled is given by area under the velocity - time graph. So, basically we have to find…

Q: (8) Given x²/3-y²/3 - y = 3, find ae equation of the tangent line at the point (1,-1).

A:

Q: a city in Africa, an epidemic spreads during 50 weeks according to the model of a sinusoidal…

A: An epidemic spreads during 50 weeks according to the sinusoidal function given in the question. To…

Q: Two cars are initially 1200 miles apart. At the same time Car A starts driving at 35 mph to the east…

A:

Q: A car is driving northwest at vmph across a sloping plain whose height, in feet above sea level, at…

A: The solution is shown in step-2

Q: Acceleration after 1 second: -12 (c) Find the acceleration at the instant when the velocity is 0.…

A: We can answer the last question as per the definition of acceleration in the below steps.

Q: Solve the problem. 23) Find the points where the graph of the function have horizontal tangents.…

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Q: (a) The curve y = 1/(1 + x²) is called a witch of Maria Agnesi. Find an equation of the tangent line…

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Q: e point P(7, 1) lies on the curve y = Vx - 6. (a) If Q is the point (x, Vx – 6), use your calculator…

A: The points P and Q are given by, P7,1Qx,x−6

Q: v = f(h) = 4/400 – h , 0 < h < 400 expresses the speed (in ft/sec) of a ball in terms of its hcight,…

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Q: A particle moves along the curve y = 6x² + 2 in such a way that its x-coordinate is changing at a…

A: Given a particle moves along a curve..Given, x-coordinate is changing at a rate of -3 centimeters…

Q: An object moves along a straight line and it's velocity (v) in ms¹ at time (t) in seconds, is given…

A: Sol:- v = 5-4t3Velocity can be written as 4t3dsdt=5-4t3ds=5-4t3dt

Q: (4 points) Suppose the position (in feet) of an object moving horizontally at time t (in seconds) is…

A: As per the guidelines we are supposed to answer only three Questions ,

Q: 2. A firefighter who weighs \(192\) lb slides down an infinitely long fire pole that exerts a…

A:

Q: The velocity (in m/s) of a hopping bunny is shown in the graph below. Describe, in words, the motion…

A: Given a velocity vs time graph of a bunny. We need to find some questions. Let's begin.