3. The velocity of a car (in miles per hour) is given by v(t) = 5 +2t, where t is in hours. Find how far the car travels during the first 2 hours.

Q: (2) From assumption (c), the velocity (v) at time (t) of the water droplet is 3. v' + t+ro If the…

A: This is a linear differential equation which have to be solved using integrating factor

Q: 2) From assumption (c), the velocity (v) at time (t) of the water droplet is 3 v' + v = g. t+ro If…

A:

Q: A particle moves on a vertical line so that its coordinate at time t is y = t – 12t + 3, t 2 0,…

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

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A:

Q: The temperature at point (x, y) is given by T(x, y) = 100 – 3x² – y³. Find the direction from point…

A:

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: Suppose that a particle moves along a straight line with velocity v(t) = 12 4t, where 0 ≤ t ≤ 2 (in…

A: For the particle moving in a straight line  Displacement 12t-2t2 Total distance travelled is 16…

Q: 9) Where is the function h(t) = (t + 5)"3 differentiable?

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 7) What is the equation of the tangent line of f(x) = xe"+ 3, at x = 0 a) Y= x+3 b) Y= 3 c) Y=…

A:

Q: 12. The position of an object at time tis given by x = V3t – 4 ++4, where x is in feet and t is in…

A: (12) The position of an objects at time t is given by  xt=3t-4+1x+4, x is in feet and t is in…

Q: If a ball is given a push so that it has an initial velocity of 24 ft/sec down a certain inclined…

A: Here we can use the fact that the velocity is the instantaneous rate of change of distance. That…

Q: Suppose that a particle moves along a straight line with velocity v(t) = 11 – 5t, where 0 <t 0.5 (-…

A: NOTE: Refresh your page if you can't see any equations. .

Q: The Strikers Technologies Company determines that the marginal cost for their MaxiPak flash disks is…

A: We will integrate the function with respect to x and then find the general solution. Next, for…

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

A:

Q: Show that the displacement after time t for motion in a straight line with constant acceleration a,…

A: Given Data: The constant acceleration is: a The initial velocity is: v0 The initial displacement is:…

Q: The position of a particle moving along the y-axis is given by y(t) = ct³ + bt + 100, where c and b…

A:

Q: Suppose that a particle moves along a straight line with velocity v(t) = 15 – 2t, where 0 ≤ t ≤ 3…

A: Here, the displacement is: S(t)=-t2+15t

Q: Assume a particle’s position is given by f (t) = −4 / t, where t is measured in seconds and f (t) is…

A: The velocity of a particle is found by differentiating the position function of a particle,…

Q: The velocity function of a particle moving along a horizontal line is given by v(t) = In2 × 23t…

A:

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: The velocity of a partical moving along x axis is defined by               v= kx3-4x2+6x where v is…

A:

Q: 9. The velocity, in kilometers per hour, of a car as it beings to slow down is given by the equation…

A:

Q: A Ferrari's position at time t is given by s(t) = t3 - 9t2 + 24t 2) What is the Ferrari's velocity…

A: Given:    s(t) = t3 - 9t2 + 24 t   Velocity at t = 0

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: Suppose that a particle moves along a straight line with velocity v(t) = 13 – 2t, where 0 <t < 3 (in…

A: Given vt=13-2t, 0≤t≤3,t=3

Q: 4) For the function p = x2y+ yz at the point (1,2,-1), find its rate of change with distance in the…

A: Given data: Function:

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

A:

Q: Suppose that a particle moves along a straight line with velocity v(t) = 7 – 4t, where 0 <t < 1.5…

A:

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: 8. Suppose that a particle moves along a straight line with velocity defined by v(t) = t2+3t – 18,…

A:

Q: The position of a particle, with respect to an initial point, after t seconds is given by the…

A:

Q: 4) The position of an object as a function of time is given by 8 = 2t + t +1 s(t) = a. Find the…

A: Definition used -                 Instantaneous velocity -  It is given by the derivative of…

Q: It is given to you that an equation of the tangent line to the graph of y=g(x) at x=4 is 4x+7y=−54…

A: Given The tangent line to the graph of y=gx at x=4 is given by 4x+7y=-54

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

A:

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

A:

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

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Q: A train moves at a velocity of v(t)= 3t" - 3200t km/sec where t in seconds is the time passed since…

A: Find your answer below

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)

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: 12 Find the slope of the tangent line, m, of g(x) = 3x2 −2x+ 4 at x = 2 a. m = 12 b. m = 3 c. m = 0…

A:

Q: 3 If the length of the curve y = 4 xž from the point (0, 0) to the point (xo, f(xo)) is L = ((20737)…

A: Given,          The length of the curve y=4x32 from the point 0,0 to the point x0,fx0           is…

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: Q2: If a body is moving along the coordinate line with velocity of: v(t) = sin(nt) 1-The position of…

A:

Q: What is the velocity at time t for a car that begins accelerating at a rate of 4 feet per second…

A: Given query is to find the velocity.

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

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Q: A particle moves in a straight line with velocity v(t)=t2 How far does the particle move between…

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

A: Given, Velocity of the particle = v(t) = 14 - 3t  We have to find the displacement at time t = 2 So,…

Q: A car moves in a straight line. At time t (measured in seconds), its position (measured in meters)…

A:

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