4. The function a(t) = 3t² – 20t + 27 describe the acceleration of a particle moving along a line. If v(t)=0 at x=1, 3, and 6, explain when the particle changes direction from left to right.

Q: • 2. Let S (t) = t3 – 12 t2 + 45 t be the position function. a. What is the velocity when…

A: We have given position function St=t3-12t2+45t Then, velocityv=dsdt=3t2-24t+45 And acceleration…

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…

Q: Suppose that a particle moves along a straight line with a velocity v(t) = 4– 2t, where t is in the…

A:

Q: If the velocity is given by : (-t^2 i + 2t^2 j+ t^2 k) then the normal component of the acceleration…

A: Given: Velocity: vt=-t2i+2t2j+t2k. Then, v't=-2t i+4t j+2t k Find the normal component of the…

Q: A particle moves along a line so that its position at any time t 2 0 is given by the function s(t) =…

A: Explanation of the answer is as follows

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: A particle starts from rest and moves in a straight line such that the acceleration, a, in m/s2 ? =…

A: To find: The instantaneous velocity at t=2. Given: The acceleration of particle is a=12t2-24t+8.…

Q: If the position of an object is s(t) = 16 + 10.5t – 4.9t meters from zero in t seconds, then what is…

A:

Q: The acceleration function of a particle moving along a line is given by: a(t) = 4t – 2 in m/s² and…

A:

Q: a particle moves according to the function s(t)= t^2 - 2t +5,  what is the instantaneous velocity of…

A: A particle moves according to the function s(t)=t2-2t+5

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

A: Given, Velocity of the particle = v(t) = 4 - 2t  We have to find the displacement at time t = 2 So,…

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: A particle moves along the x-axis with an acceleration given by a(t) = 7t + 8, where t is measured…

A:

Q: If the position of a moving particle at any time 't' is defined by s(t) 3t-9t,0<t<6. The…

A:

Q: A particle moves along the x-axis with velocity given by v(t) = 6t² + 4t + 14 for time t > 0. If the…

A: Convert velocity into distance and time

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: 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: solve using ODE from t=0 to 2 when y(0)=1 dy/dt= yt^3 - 1.5y

A:

Q: A particle moves along the x-axis with its position measured relative to the origin and has an…

A: To find: The velocity and position after t=1 second: Given: The acceleration of the body is at=6t+4…

Q: 8. The temperature of the xy-plane is given by the function f(x, y) = x²y+e¬¤. (a) At the point…

A: The direction of maximum decrease of a scalar function f(x, y) is given by the negative of the…

Q: t)=2t^2 +6t-5 is the velocity of an object over time what is the acceleration of the object at t=2

A: Given query is to find the acceleration of the object.

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

A:

Q: A particle moves along a straight line and has acceleration given by s"(t) = 5t +3- Its initial…

A: Given,  s''(t)=5t+3, s'(0)=-4, s(0)=7

Q: Show that for motion in a straight line with constant acceleration a, initial velocity v0, and…

A: Let the acceleration a(t) = a, constant.Take integral on both sides to get velocity equation,

Q: Determine D,f(3,-1,0)for f(xy.z) = 4x-y'e in the direction of i = (-1,4,2, (Express your final…

A:

Q: Find the displacement of a particle moving in a straight line with velocity v(t) = 4t - 3 mis over…

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

Q: If the position of a moving particle at any time t' is defined by s(t) = t - 2t2 + 13. Then the…

A:

Q: If the velocity is given by : (-t^2 i + 2t^2 j+ t^2 k) then the normal component of the acceleration…

A:

Q: The movement of a particle from time t=0 to t=4 is given by the equation s(t)=−5t2−10t−6. What is…

A:

Q: The position function of a particle is given by s(t) = 3t2 - t°, t 2 0. (a) When does the particle…

A: This question is based on derivative application.

Q: 7. A particle starts from rest and moves in a straight line such that the acceleration, a, in m/s²…

A: Given a particle starts from rest and moving along straight line has acceleration a is given as:…

Q: A particle moves along the x axis with position measured relative to the origin and has an…

A: Consider that acceleration of object is given by at=6t+4 cm/s2, initial velocity is -6 cm/s and…

Q: According to one model that attempts to account for air resistance, the distance s(t)(in meters)…

A:

Q: 3. The position of a particle travelling along a horizontal line in t seconds is s(t) = 2t° – 15t –…

A: Velocity and acceleration from displacement function of time t

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

A:

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: A particle moves along the x-axis with velocity given by v(t) = 3t2 + 12t – 6 for timet > 0. If the…

A:

Q: #2. Consider the function f (x, y,z) = xy+3xz² + 5y at the point (1,0, 2) (a) Find the direction in…

A:

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: Determine the position function if the acceleration function is a(t) = 6sin t+5, the initial…

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Q: Find the directions in which f(r, y) = (r+y-2)2+(3x- y- 6)?, increase and decrease most rapidly at…

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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 position function of a particle is given by s (t)= 3t2-t3, t greater than or equal to 0. a.…

A: The position function of a particle is s(t)=3t2-t3, t≥0

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

A:

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

A:

Q: At time 0<t< 2, the velocity of a particle moving along the x-axis is given by v(t)= tsin(tcubed). b…

A:

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

A: