A particle is moving with acceleration a(t) = 18t + 8. its position at O is s(0) = 4 and its velocity at time t = 0 is v(0) time t 13. %3D What is its position at time t = 7?

Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A: Given,

Q: where w(t) is measured in 74 (c) The grain in the silo is spoiling at a rate modeled by w(t) = 32 ·…

A: c) To find : The amount of grain remain unspoiled in the silo at time t=8 Given that : The amount of…

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A: We will use the maximum height formula Where u=initial velocity. g=gravity H_max= maximum height

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A: Definition used -                   v=∫adts=∫vdt

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Q: Find velocity (f'(x)) and acceleration (f''(x)) at time or t=0 with equation s(t)=2((e^t)-(e^-t))

A: We have to find velocity and acceleration

Q: dv dt    = −kv2 An object moving through the water has an initial velocity of 40 m/s. Two seconds…

A: As the given differential equation is: dvdt=-kv2 Given conditions are:  t=0 , v=40 mst=2s, v=30 ms…

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Q: 2. Suppose s(t) is the position of an object moving along a line at time t > 0. Describe a process…

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A: To find the equation for velocity we will integrate the equation of acceleration  c=integrating…

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Q: A particle is moving with acceleration a(t)=12·t+3. At time t=0, its position is s(0)=7 and its…

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A: Let w de the distance between origin and the particle at any time t. Given that, dwdt=11 Now by…

Q: A 32-lb weight stretch a spring 2ft. At t = 0, the mass is released 1 ft above the cquilibrium…

A: The solution is given below

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A: Given velocity of particle is vt=4t-3. To find the dispalcement of particle over time interval 2,5.…

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Q: 1. The position of a particle at time t is given by s(t) = t³ – t2. Using a table, estimate the…

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Q: Suppose that a furniture removal truck gradually speeds up so that for the first 10s its…

A: We will find out the required values.

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Q: What is the position at time t of a car that is accelerating at a rate of 5 meters per second…

A: To determine the position of the car from the given data. (note that s =20 when t=2, not as given)

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A: Given: v(t)=t2ln(t+2)we know that acceleration of particle is differentiation of velocity of…

Q: .................... ..................... A new fast-food firm predicts that the number of…

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Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A: Given that, dndt=6t+1 where t is the number of years, 0≤t≤15

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Q: A particle moving along a line has position s(t) = t4 − 18t2 m at time t seconds. At which times…

A: St=t4-18t2The particle passes through the origin when St=0t4-18t2=0t2t2-18=0t2=0   t2-18=0⇒t=0…

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Q: - If a particle's position at a time t is given by f (t) = t³ + 1, i. Find its average velocity over…

A: f(t) = t3 + 1 i. Average velocity over the interval [-1,1] is given as

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Q: The position of a particle at time t is s(t) = 4t^3. compute the average velocity over the time…

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Q: The height (in centimeters) at time t (in seconds) of a small mass oscillating at the end of a…

A: Height is given by ht=3 sin 2πt→1instantaneous velocity=dhdt⇒Differentiate eqn 1 , w.r.t 't' , we…

Q: A ball is thrown upward from a height of 1.5 m at an initial speed of 45 m/sec. Acceleration…

A: Given that the initial speed=v0=45Initial height=h0=1.5Acceleration=a=-9.8So using the relation…