Suppose that a particle moves along a straight line with velocity v(t) = 14 – 3t, where 0

Q: (a) If F(x) = 6x/(2 + x2), find F '(2) and use it to find an equation of the tangent line to the…

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Q: Suppose that a particle moves along a straight line with velocity defined by v(t) = (10t(4 − t))/((t…

A: to find the displacement of the particle , integrate the velocity function vt therefore,…

Q: Find the equation for the line tangent to g(x) rcos(x) at x = 0

A: Given:The function g(x) = (x cos(x))/(x+2).Obtain the tangent line for the above function at x = 0.

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

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Q: The displacement (in meters) of a particle moving in a straight line is given by s = t2 - 8t + 17,…

A: We have solve the problem by putting the value of interval in average velocity formula.

Q: The displacement (in meters) of a particle moving in a straight line is given by = 9t3 + 4t – 18, |…

A: Given,         The displacement in meters of a particle moving in a straight line is given by…

Q: A particle that moves along a straight line has velocity v(t) = t²e-5t meters per second after t…

A: Given a particle that moves along a straight line has velocity v(t)=t2e-5t

Q: b) Use the velocity function v(t) = 2e" to compute the distance traveled by an object over the time…

A: The detailed solution is given below  Thank you

Q: Solve the problem. A body of mass m is moving in a straight line with an initial velocity of 2 m/s…

A: Given:-   acceleration⇒6t2-2t+4initial  velocity  of 2m/sec  from origin at  t=0,a=acceleration;…

Q: Suppose the velocity function of a particle is given by y = 2 – t - t2 at any time t ( time is in…

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Q: Let v(t) = -13t + t² be the velocity, in ft/sec, of an object at time t, in seconds. a) What is the…

A: Given velocity function, v(t)= -13t + t²

Q: If a cannonball is shot directly upward with avelocity of 256 ft per second, its height above the…

A: Given: st=256t-16t2 We know that velocityvt and accelerationat is respectively first and second…

Q: If a balloon is thrown directly upward with a velocity of 96ft/s, its height (in feet) after t…

A: Height of balloon after t seconds is…

Q: What is the velocity and distance covered in 5 seconds when acceleration is 0.02s^(-7/8)) m/s²,…

A: Given:    a = 0.02s(-7/8)     t = 5 sec

Q: A particle moving along a line has position s(t) = t 4 - 18t2 m at time t seconds. At which times…

A: st=t4-18t2 Substitute 0 for s(t) into above position function. st=0t4-18t2=0t2t2-18=0t=0 or t2=18t=0…

Q: A particle is moving such that its position after t hours is s(t) =- -measured in meter. 4t +1 Find…

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Q: The velocity of a particle moving along a straight line is given by v(t) = 6t² + 4t – 5 cm/sec at…

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Q: Suppose that a particle moves along a straight line with velocity v(t) = 12 – 3t, where 0 <t < 0.5…

A: Solution

Q: A ball is thrown upward from a height of 6.5 m at an initial speed of 61 m/sec. Acceleration…

A: here we have .................initial height .................initial velocity ..............gravity

Q: With time t in seconds, the velocity of a bicycle, in feet per second, is given by At) = 4t. How far…

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Q: If a baseball is thrown upward with a velocity of 45 m/s, its height in meters t seconds later is…

A: We know that, Average velocity          = change in position/time elapsed.

Q: Suppose that a particle moves along a straight line with velocity v(t) = 10 - 5t, where 0 ≤ t ≤ 1.5…

A: The answer as follows:

Q: A particle moves along the x-axis with velocity given by v(t)=3t^2-6tv(t)=3t2−6t for time t\ge…

A: Answer and explanation is given below..

Q: A particle starts from rest and moves in a straight line such that the acceleration, a, in m/s^2 is…

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Q: If a ball is thrown into the air with a velocity of 14 m/s, its height (in meters) after t seconds…

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Q: A particle is moving along a straight line so that v ft/sec is the velocity of the particle at t…

A: Given v=t+3t2+3t+2. The objective is to find the distance traveled by the particle from the time…

Q: A ball is thrown upward from a height of 0.9 m at an initial speed of 24 m/sec. Acceleration…

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Q: Suppose that a particle moves along a straight line with velocity v(t) = 7 - 3t, where 0 ≤ t ≤ 0.5…

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Q: The distance of a body travels as a function of time and is defined by x(t) = 18t + 9t^2. What is…

A: Given that: Distance travelled by the body is given by:             x(t)=18t+9t2

Q: * The velocity of a particle moving on a straight line is given by v(t) = t²e¯† meters per second at…

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Q: A particle moves along the x-axis with velocity given by v(t) = 6t2 – 18 for time t > 0. If the…

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Q: Find an equation for the instantaneous velocity v(t) if the height of an object is defined as h(t)…

A: To find: The instantaneous velocity at any point in time. Given: The height of an object is .…

Q: The velocity function (in meters per second) is given by v(t) = t2 - 2t - 3, for a particle moving…

A: We will use formula for the Displacement and distance in terms of Velocity function

Q: Given the acceleration of an object and its initial velocity, how doyou find the velocity of the…

A: We know that the rate of change of velocity of a moving particle is known as its acceleration. Let…

Q: A cyclist rides down a long straight road at a velocity (in m/min) given by v(t) = 400-20t, for 0≤t≤…

A: Given query is to find the distance traveled for different times.

Q: Suppose you are standing in a field near a straight section of railroad tracks just as the…

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Q: Suppose that a particle moves along a straight line with velocity v(t) = 10 - 1t, where 0 <ts 3 (in…

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Q: Find the slope of the tangent to Ax) = x²e* at the point (1, e). a) e b) 1 c) 3e d) 2 + e

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Q: A particle moves along the x-axis with velocity given by v(t) = 6t² + 1 for time t > 0. If the…

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Q: Researchers in Alaska have developed models that can be used to estimate the mass of a polar bear.…

A: The equation relating mass and body dimensions is given as: M(x,y)=0.000199x1.2823y1.4874   Weight…

Q: 4x Find the equation of the line tangent to y = e at x =- In 5.

A: Problem related to application of derivative

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 particle is moving in a straight line with the velocity v(t) =1-t,0<t< 3. Compute the distance…

A: We have V=1-t⇒dxdt=1-t∫0△xdx=∫(1-t)dt

Q: Suppose that a particle moves along a straight line with velocity v(t) = 14 – 2t, where 0 <t < 3 (in…

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Q: Let v(t) = t2 – 10t be the velocity, in ft/sec, of an object at time t, in seconds. a) What is the…

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Q: Suppose that a particle moves along a straight line with velocity v(t) = 13 - 5t, where 0 ≤ t ≤ 1…

A: Here the velocity function is v(t)=13-5t   , where 0≤t≤1 (in meter per second). We have to find the…

Q: Suppose that a particle moves along a straight line with acceleration defined by a(t)=t-3 where…

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Q: Find an equation of the line tangent to f(x) = Va at (4, 2).

A: equation of tangent line

Q: Suppose that a particle moves along a straight line with velocity v(t) = 9- 6t, where 0<t< 0.5 (in…

A: Given: v(t) = 9 - 6t, t = 0.5s