4. The position of a particle travelling along a horizontal line in t seconds is s(t) = 2t3 – 15t² – 144t + 7 meters. (a) Determine the time intervals when the object is slowing down or speeding up. (b) Determine the acceleration of the particle when the velocity is 0.

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

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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: 3. The position of a particle travelling along a horizontal line in t seconds is s(t) = 2t³ – 15t² –…

A: Use the application of derivative to determine velocity and acceleration.

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Q: s(t) = 2t – 15t2 + 36t – 10represents the position of a particle travelling along horizontal line.…

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A: use simple velocity,acceration,and distance formula.

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Q: s(t)%3D512 +t3 :-

A: Given information: st=5t2+t3 Find the velocity at -2.

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A: Convert velocity into distance and time

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

Q: 2. Suppose s(t) is the position of an object moving along a line at time t > 0. Describe a process…

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Q: A particle moves along the x-axis with velocity given by v(t) = 10t + 12 for time t> 0. If the…

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Q: EX-4- A particle moves along a straight line so that after t (seconds), its distance from O a fixed…

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A: Answer and explanation is given below..

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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…

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Q: Suppose that a particle moves along a line with position function s(t) =2t^2 +3t+1 where s is in…

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

Q: A particle moves along the x-axis with velocity given by v(t) = 10t + 12 for time t> 0. If the…

A: Given: The velocity of the particle along x-axis is vt=10t+12 The particle is at the position x=2 at…

Q: 4. The position of a particle travelling along a horizontal line in t seconds is s(t) = 2t3 – 15t² –…

A: (a) consider the given displacement function, st=2t3-15t2-144t+2 use the following formula to find…

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A: Let's find.

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A: This is a problem related to differentiation of the function. Based on the general formula and…

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Q: 4. The position of an object at time t is given by x = 34f - 8t + 2, where x is in feet and t is in…

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

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Q: 6. The acceleration of a body moving in a straight line is given in terms of timet by a(t) = 8-6t If…

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

Q: A particle moves along the x-axis with velocity given by v(t) = 6t² – 10t for time t> 0. If the…

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

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