At time t, the position of a body moving along the s-axis is s=3- 212 + 120t m. Find the body's acceleration each time the velocity is zero.

Q: The position of a body moving along s-axis at any time 't' is given by s(t) = 9t3 – 48t, then the…

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Q: What is the daredevil’s acceleration at t = 3 seconds?

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Q: The position of a moving object is s(t)=t^3-2t^2-8t+5 feet away from 0 at t minutes. How long, in…

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Q: Let r(t) =. Describe the motion of a particle following this path. What happens to its speed as time…

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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 particle moves vertically (in inches) along the yaxis according to the position equation s(t) = -…

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Q: d. Without doing any computations, what do you expect to be the instantaneous velocity of the ball…

A: Since   s(t) = 64 - 16(t - 1)² As we can see that at t = 1 , the above quadratic equation has its…

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: The time of oscillation, 1, of a pen- dulum is given by t 27 1. wherel is the length %3D of the…

A: Write this equation in standard form then diffrenciate.

Q: A particle moves with position function s = t4 – 4t3 20t2 + 20t, t > 0 - (a) At what time does the…

A: Given problem:- A particle moves with position function   S=t4 -4t³ - 20t² + 20t, t≥ 0   (a) At what…

Q: The acceleration of a particle at time t is given by a(t) = 4e2t¸ If the initial velocity was 5, and…

A: We will use integration to first find the velocity and then integrate velocity function to find…

Q: The temperature at a point on a metal surface is T (x, y. z) = 0.05x² – 0.01y³ – z in degrees…

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Q: Find the displacement of a particle moving in a straight line with velocity v(t) = 4t − 3 m/s over…

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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: 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: A particle moves along a coordinate line in such a way that its velocity at any time t is given by…

A: We have, a particle moves along a co-ordinate line in such a way that its velocity at any time t is…

Q: A parachutist of mass m falls from rest in the Earth's gravitational field and is subjected to mg…

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Q: Suppose that the velocity of a falling body is y = k√s m/sec (k a constant) at the instant the body…

A: The velocity (y) of a falling body is  where k is a constant and s is the function that represents…

Q: A particle starts moving from the origin with the velocity v(t)=⟨4t,3t2−1⟩, where t is measured in…

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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: Two particles have positions at time t given by s =4t-t^2 and s=5^2-t^3. Find the velocities v1 and…

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

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Q: A ball is thrown upward from a height of 12.5 m at an initial speed of 30 m/sec. Acceleration…

A: Consider the height: H=12.5 m and initial speed: u=30m/sec The velocity function is given by v(t)=…

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: 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: 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: A particle leaves the origin with its initial velocity given by v=23.8i - 143 m/s, undergoing…

A: Topic = Algebra

Q: A ball is thrown upward from a height of 1.5 m at an initial speed of 25 m/sec. Acceleration…

A: g = -9.8 m/s2 v0 = 25 m/s h0 = 1.5 m   h(t) = -(g/2)t2 + v0t + h0 h(t) = -4.9 t2 + 25 t + 1.5…

Q: A particle is thrown vertically upwards in the air. The distance it covers in time t is given by…

A: We will be using the fact that rate of change in distance is called velocity. v(t)=dsdt

Q: A volleyball is moving 16 m/s at 25o North of straight down. If +x is East, +y is North, and +z is…

A: Draw the sketch, as follows: Since the ball is moving 25° North of "Straight Down" direction, its…

Q: A particle moves along a straight line with equation of motion s = t – 1tª Find the value of t…

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: The position of a body moving along s-axis at any time 't' is given by s(t) = 16t3 – 12t, - then the…

A: We will find out the required value.

Q: Suppose velocity of a car starting from rest is modelled by equation V(t)= In(4t^3 + 1) m/s What…

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Q: Q-1-At time t, the position of a body moving along the s - axis is t4 9. S = - 2t3 2t3 +t2 + 5t -- 4…

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

Q: An object with an initial velocity of 40 m/s undergoes an acceleration of a(t) = 12t – 10 m/s“, t…

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Q: A sky diver weighing 192 lb (including equipment) falls vertically downward from a very high…

A: Given:

Q: Find the position of the particle at time t=4. Is the particle moving toward the origin or away from…

A: If the velocity function is given then by integration we will calculate the position of the particle…

Q: A particle moves on the 0x axis with acceleration proportional to velocity. Assuming that v(0) = 3,…

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Q: A ball is thrown upward from a height of 4.6 m at an initial speed of 48 m/sec. Acceleration…

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Q: A Ferrari's position at time t is given by s(t) = t3-9t2 + 24t 4) At what time is the acceleration…

A: Given the equation of position of Ferrari's s(t)=t3−9t2+24t    ....(1)

Q: the velocities when they have the same acceleration.

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Q: Q 10 Show that for motion in a straight line with constant acceleration a, initial velocity vo , and…

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

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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: If the velocity function v(t) of an object is at its maximum, then the value of a(t), its…

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Q: A ball is thrown upward from a height of 1.5 m at an initial speed of 45 m/sec. Acceleration…

A: Given that the initial speed=v0=45Initial height=h0=1.5Acceleration=a=-9.8So using the relation…

Q: 40 m/s a. -1/T

A: We integrate acceleration to find velocity and to find position we integrate the velocity

Q: A spring is stretched 12 inches by a 24-pound weight. If the weight is pulled 10 inches below the…

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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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