A particle follows the trajectory x(t) = t3 + 2t, y(t) = 10t – t2 with t measured in seconds and distance measured in centimeters. When does the particle hit the ground? sec How far is the particle from the origin when it hits the ground? cm

Q: find an equation for the line in the xy-plane thatis tangent to the curve at the point corresponding…

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Q: A particle is moving along a straight line with velocity v(t) = t2 - 2t. Its distance from the…

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Q: d?y 1 C. Given vx +Vy = 2, show that dx2 3 x2 D. Find the equation of the tangent line to the curve…

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Q: The velocity function (in meters per second) for a particle moving along a line is given by v(t) =…

A: Given, v(t)=t3-2t2   Interval [a,b]=[-2,3]

Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = -3t2 - 2t +…

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Q: 2. A particle is moving along a horizontal line such that its velocity is given by v(t) = 3t? –…

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Q: a) What is the particle's position at time 2? b) What is the particle’s displacement from t= 1 to…

A: (a) The function representing the position is  X(t)=t3-15t2+48t. To find the position of the…

Q: A drone traveling horizontally at 80 m/s over flat ground at an elevation of 3500 meters must drop…

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Q: Find the velocity of a particle when  S = t2 + 3t - 4 at t = 1 sec

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Q: The position of a particle is given by: s = f(t) = t³-12t²+36t, 2. where t is measured in seconds…

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Q: A point moves along a straight line (xy) so that its distance s(cm) from the point x at time t(sec)…

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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: A particle moves along the x-axis with the origin as the reference point so that at time t in…

A: Recall what Newton said to us: Velocity = rate of change of position Hence, v(t) = dx/dt

Q: t 2 If the velocity of a moving object is y(t) = --- 2 12 in meters per second, then what is its…

A: The veloctiy of a moving objcet is v(t)=t2-2t2 in meters per second.

Q: A particle moves on the x-axis with velocity given by v(t) = 3t4 − 11t2 + 9t − 2 for −3 ≤ t ≤ 3 .…

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Q: 21. A particle follows the trajectory x(t) 4 t3 +2t, y(t) = 201 – 12 with t in seconds and distance…

A: The trajectory of particle is given as

Q: The tank in the form of a right-circular cone of radius 11 feet and height 15 feet standing on its…

A: Given: Let us consider the right-circular cone, Radius=11 feet Height=15 feet and circular hole of…

Q: Suppose an object moves along the x-axis so that its position at time t is x = −t +t3/6 (a) Find…

A: Note: There are many subparts in the questions so I will answer the first three questions and other…

Q: An object experiences acceleration as given by: a(t) = e3t – 2, v(0) = 1 and y(0) = 3 %3D Determine…

A: We can solve this question and find the value of displacement and velocity as below

Q: The position of the particle at time t is given by s(t) = t² – 18t + 80. %3D The particle is moving…

A: The particle will move from left to right if the velocity is positive

Q: At time t=0, a driver jumps from a diving board that is 25 feet high. Because the drivers initial…

A: Given, Position function, h(t) = -16t2+15t+25 a) When the diver hit the water, h(t)=0…

Q: A particle moves along the x-axis with velocity given by v(t) = 6t2 at time t = 0, what is the…

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Q: A) The position of a particle P(x, y) at time t is given by: (2t + 3)7 y +t . Find the distance it…

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Q: If the position of a particle is represented by x(t) = -t2 + 1, what is its instantaneous velocity…

A: We are given that the position of a particle is represented by x(t)=-t2+1. Now, we need to find its…

Q: The position of the particle at time t is given by s(t) = t2 - 8t + 15. The particle is moving from…

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Q: At time t sec, the positions of two particles on a coordinate line are s1 = 3t3 - 12t2 + 18t + 5 m…

A: To find velocity we have to differentiate the distance s with respect to t.

Q: The position function of a particle is given by s(t) = 3t2 – t3, t > 0. (a) When does the particle…

A: The given position function is:  s(t)=3t2-t3So, the velocity function…

Q: A particle moves along the x-axis so that at time t> 0 its position is given by x(t) = -t3 +11t?…

A: For the given position vector  x(t) = -t3+11t2-24t Velocity at t = 7 is calculated as shown below

Q: The position function of a particle is given below. s(t) = 3 + 6t2 - 61t, t > 0 When does the…

A: Velocity function is the derivative of the position function. So differentiating s(t) with respect…

Q: 9) A particle moves along the y-axis with velocity v(t) = 2tvt² +1 m s' for t 2 0. Describe its…

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Q: dy of the curve yln x + 5x² + y' = 13 at the point (1,2) dx b) Find

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Q: A rocket accelerates by burning its on-board fuel, so its mass decreases with time. Suppose the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3t/2 Find the length, s, of the parameterized curve, x =3 e ° - 4t, y = 8 e 3t over the interval…

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

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Q: A particle moves along a straight horizontal line so that its position at any time is given by s(t)…

A: Let's find.

Q: At time t, the position of a body moving alongthe s-axis is s = t3 - 6t2 + 9t m. Find the total…

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Q: An object moves on a horizontal coordinate line. Its directed distance s from the origin at the end…

A: Please find attachment for the details solution

Q: (2.;v3). 1 Find the equation of the tangent line to x? +y²: = 1 at Use exact values in y = mx + b…

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Q: The position function of a particle is given by = t3 – 10.5t2 – 2t, t > 0 When does the particle…

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Q: (a) What is the particle's position at t = 0? (b) What is the particle's position at t = 3? (c) What…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: The displacement (in meters) of a particle moving in a straight line is given by s = t2 – 3t + 10…

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Q: A heat-seeking particle is located at the point (2, 3) on a flat metal plate whose temperature at a…

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Q: If position is given by p(t)=-t^2+5t what is the velocity v(t) at t=2?

A: The position is p(t)=-t2+5t

Q: The position of the particle at time t is given by s(t) = t – 6t + 8. %3D The particle is moving…

A: The particle moves to right if it's velocity is positive .

Q: A particle moving on a line is at position x(t)=t3−9t2+24t−5 at time t where t is in seconds. At…

A: The given function for position of an object is where t is the time in seconds. Now, to find points…

Q: the velocities when they have the same acceleration.

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Q: A particle in R2 has a velocity function of v(t) = (3t²-4, 6t + 2) (given in m/s). After moving for…

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Q: An object experiences acceleration as given by: a(t) = e3t – 2 , v(0) = 1 and y(0) = 3 Determine the…

A: Given,          An object experiences acceleration as given by :          at=e3t-2 , v0=1 and y0=3

Q: The position of a body moving along s-axis at any time 't is given by s(t) = 4t- 12t, then the…

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