Let s(t) = 6t° – 81t + 360t be the equation of motion for a particle. Find a function for the velocity. v(t) = Where does the velocity equal zero? [Hint: factor out the GCF.] t = and t Find a function for the acceleration of the particle. a(t) =

Q: The motion of the particle is given by the equation v (t) = 2.00 t² – 3.20 t³ . What is the…

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Q: Let s(t) = 6t° – 72t² + 270t be the equation of motion for a particle. Find a function for velocity.…

A: s(t)=6t3-72t2+270t v(t)=ds/dt a(t)=dv/dt

Q: Find the differential of the function. p = 39 - 8q3/2 dp 252.81

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Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

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Q: An insect is in a toxic environment. The level of toxicity is given by T(x,y)= 2x* – 4y° If the…

A: Tx=0⇒x=0Ty=0⇒y=0Using D-TestD=TxxTyy-[Txy2]D=0 at (0,0)   T(x,y) is minimum

Q: The acceleration of a moving particle at any time t is given by expression 6t – 24. Find the…

A: given acceleration a(t)=6t-24

Q: The position function of a particle is giyen by s(t) = (t – 1)²(t – 3) , where t is measured is…

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Q: The position of a particle is given by s(t) = t³ – 20.5t² – 2t, t > 0. When does the particle reach…

A: Given,           The position of a particle is given by st=t3-20.5t2-2t , t≥0.             The…

Q: The position function of a particle is given below. s(t) = t³ + 1.5t² - 55t, t z 0 When does the…

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Q: If the position of a particle at a time t is given by the equation x(t)=t^3-11t^2+24t , find the…

A: If the position of a particle at a time t is given by the equation x(t)=t3-11t2+24t We have to find…

Q: For t 0, the velocity of a particle moving along the raxis is given by e(t)-e- 6r+ 10t-4. A what…

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Q: A weather balloon is released and rises vertically such that its distance s(t) above the ground…

A: s(t)= 6+13t+8t^2 ds/dt = v = 13+16t v= 13+ 16(52) v= 13 + 832 v= 845.

Q: The position of a moving object is s(t) =t² - 3t-9t-1 meters to the right of 0 in t séconds. (a)…

A: Velocity of  an object is derivative of position s with respect to time t. Object is at rest when…

Q: Suppose the height of a rocket rising vertically from the ground is modelled by the equation; S(t)=…

A: Here equation is S(t)=t2+2t+4A)we have S(t)=t2+2t+4put t=1 and t=8 in…

Q: B) Find the approximate roots of the following equation: f(x) = x3 – 8 = 0, on the closed interval…

A: Roots of an equation f(x): roots of an equation are those values of x for which the function f(x) =0…

Q: If s(t) =t ––t² +2t – 5 represents the position of a yo-yo off the ground then when %D would the…

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Q: The position function of a particle is given by s = t3 – 13.5t2 – 4t, t>0, where t is measured in…

A: Given: s=t3-13.5t2-4t,   t≥0 The velocity given is 26m/s Since, vt=s't Therefore,…

Q: The position function of a particle is given below. 6t2 91t, t 2 0 s(t) t3 When does the particle…

A: To determine the time when the particle reach a velocity of 5 m/s.

Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

A:

Q: The velocity of a moving particle at any time t is given by expression 12t2 + 10t +7. If when t =…

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Q: A particle moves along a straight line with equation of motion = f(t) = 9t2 + 4t + 5, where s is…

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Q: 6. Find the equation of the motion. 12 and s=3, v=1, when t=2 t4 Given: a ==

A: Given: a=12t4  ……1   Also, At t=2:v=1……2At t=2:s=3……3

Q: A particle moves vertically (in inches) along the yaxis according to the position equation s(t) =° –…

A: We have to find value of t

Q: The position function of a particle is given by s(t) = 3t2 – t°, t > 0.

A: The position of particle is s(t)=3t2-t3, t≥0 Note:   Multiple questions are given, we are answered…

Q: A rock is thrown vertically upward with a velocity of 256 ft/s, so its position function can be…

A: A rock is thrown vertically upward with a velocity of 256 ft/s, Its position function can be modeled…

Q: The position function of an object is given by s(t)%3D21 - 5t, where time, t, is in seconds and…

A: Position function st=2t3-5t

Q: Let s(t)=4t^3+48t^2+180t be the equation of motion for a particle. Find a function for the velocity.…

A: This function is related to motion of partical. Solve in step 2.

Q: - The position of an object moving on a line is given by s(t) = 6t2 – t°, t > 0,

A: Solve

Q: given the position function for an object in motion  is s(t)=-4t3+4t2-1 then the accelaration at t=1…

A: Differentiate the position function with respect to time t.

Q: A body moves on a coordinate line such that it has a position s=t2-3t+2 on the interval 0≤ t≤ 4…

A: You know, v=dsdta=dvdt

Q: In an electric circuit containing a resistor and a capacitor with an initial charge qo, the charge q…

A: Given

Q: A weather balloon is released and rises vertically such that its distance s(t) above the ground…

A: Given data: The expression for the distance of the balloon is s(t)=6+2t+t2. (a) The expression for…

Q: The position function of a particle is given below. s(t) = t3 + 1.5t2 - 16t, t 0 When does the…

A:

Q: The displacement (in meters) of a particle moving in astraight line is given by the equation of…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: If the position of a hummingbird flying along a straight line in t seconds is given by s(t)=-3t +4t?…

A:

Q: Find the differential of the function. p = 3q – 8q3/2 dp =

A: SOLUTION-

Q: The position of an object at any time t is given by s(t)=33t^4 − 40t^3 + 126t^2 −9. (a) Determine…

A: Position of an object is s(t)=33t4−40t3+126t2−9. (a) The velocity is the rate change of position of…

Q: Find the velocity and acceleration when t = 3. %3D X =t° -3t –5

A: Solution is given as below:

Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

A: Given query is to find the the distance when velocity is same.

Q: Find the equation of the tangent and the equation c 3x+1, Equatio O a. Equation of Tangent: y = O b.…

A: Equation

Q: Let s(t) = t3 - 6t2 + 12t be the equation of motion for a particle. a) Find the velocity at time,…

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Q: Suppose the position equation for a moving object is given by s(t) = 6t² – 5t + 4 where s is…

A:

Q: If y1=2x+4 and y2 =x^2+C, find the value of C such that y2 is tangent to y1

A: Given: y1=2x+4    and    y2 =x²+C   To find :the value of C such that y2 is tangent to y1

Q: An insect is in a toxic environment. The level of toxicity is given by I(x,y)= 2x* – 4y If the…

A:

Q: The equation of the tangent to the curve y = x4 – 4x3 + 2x? – 4x + 15 that is perpendicular to the…

A: topic - equation of tangent line to curve

Q: The position of a particle moving along the x-axis at any time t in seconds is given by x(t) = -2t2…

A: x(t)=-2t²+3t+5 To find the (a) position, (b) velocity and (c) Acceleration at t=5

Q: Q2: Find the slope of the curve r = -1 + cos 0 0-T/2

A:

Q: A woman bails out of an airplane at an altitude of 10,000 ft, falls freely for 22 s, then opens her…

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Q: Find the linear approximation to the equation f(x, y) = 4xy – 6xy? at the point (2,1,-4), and use it…

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Q: Let s(t) = t2+2 be the position of a car on a road, where s(t) is in feet and t is in seconds.  Find…

A: Given,