The position of a particle is given by the hourly equation: x=t³-t²+3t-7, in meters. Determine demonstrating his reasoning: a) Your average speed between instants t = 0 and t = 3.0 s; b) Its average acceleration between the moments t =1.5 s and t = 2.5 s; c) Its instantaneous acceleration at instant t =2.0 s; d) In which instant(s) the particle inverts the direction of movement? If there is no this(s) instant(s), prove it.

Q: 11.14 It is known that from t = 2 s to t = 10 s the acceleration of a particle is inversely…

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Q: instantaneous acceleration at t = 2.1s of partide whose position is given by y(t) = - 4.1t ^ 2 + 6.7

A: Given  Position of particle  y (t) =-4.1 t2  + 6.7

Q: The velocity function of a particle moving along a horizontal line is given by v(t) = t2-8t+15,…

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Q: The position ? of a particle along a straight line is given by s = sin(0.4t) - 10t + 20t2 , where s…

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Q: An object has an initial velocity 4.3î + -3.7j m/s. Over a v1 = period of time t= 1.4 s, its…

A: Given, v1→=4.3i^-3.7j^v2→=-2i^+0.5j^  t= 1.4 s

Q: The displacement of a particle is 18t+5t^2. Calculate the instantaneous velocity at t=2 and t=3

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Q: The position of a particle moving along the x-axis is described by x = t3 – 108t in where t is the…

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Q: the motion of the particle is described by the equation x(t)=at^3-bt^2. where a is 3.36 in m/s^3 and…

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Q: The position x of a particle in motion, as a function of time t, is given by: x = 3t 2- 2t + 2. %3D…

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Q: A particle moves along the yy axis so that its position at any time t, for 0≤t≤5t, is given by…

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Q: Consider the position function ​s(t) = -4.9t2 + 31t + 20. Complete the following table with the…

A: a)the average speed is,

Q: The rectilinear motion of a particle is governed by the equation a = 6t – 4 where a is in m/s^2 and…

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Q: A particle moving along a line has position s(t) = t4 − 18t2  at time t seconds. At which times does…

A: Introduction: The velocity is defined as the rate change of the position of the object with respect…

Q: What is the instantaneous acceleration at t=2.1 s of a particle whose position is given by…

A: Given The position of the particle is given as We have to find the instantaneous acceleration at t…

Q: The position of a particle at time t (s) is s(t) = √(t2 + l)m. Compute its average velocity over [2,…

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Q: Two particles are currently in motion along parallel, straight paths in the positive x-direction,…

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Q: The position of a particle is 7(t) = (2.0t21-3.0t Jm.What is the magnitude of the acceleration (in…

A: Acceleration is constant which means that acceleration is not the function of time (it will not…

Q: A particle's position is given by x = 6.00 - 15.00t + 3t², in which x is in meters and t is in…

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Q: The position in metres (as a function of time, in seconds) for a particle moving along the x-axis is…

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Q: The position of a particle as it moves along the x axis is given, for t > 0, by x=(t^3−3t^2+6t) m…

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Q: Two particles move along an x axis.The position of particle 1 is given by x = 6.00t2 + 3.00t + 2.00…

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Q: Suppose that the position of a particle is given by s = f(t) = 2t³ + 6t + 9. (a) Find the velocity…

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Q: The box slides down the helical ramp which is defined by r = 0.5 m, theta = (0.5t^3)rad, and z = (2…

A: We have r=0.5 m, θ=0.5t3 rad and z=2-0.2t2m. We need to find velocity and acceleration. They can be…

Q: The position of a particle is defined by r ={4(t - sin t)i + (2t^2 - 3)j} m, where t is in seconds…

A: Derive the provide equation wrt to time, t and determine the velocity vector of the particle.

Q: The motion of a particle from a fixed point is defined by the equation v = (3t-1)(t-1), where v is…

A: Given data: Velocity of the particle, v=3t-1t-1m/s Time interval, t=3 s For t=2 s; x=0

Q: The position of a particle moving along the x axis is given by x = 3t2 - 12t - 20m, where t is in s.…

A: Average acceleration is defined as the time rate of change of velocity,aavg.=∆v∆t Average velocity…

Q: 2.57 • CALC The position of a particle between t = 0 and t = 2.00 s is given by x(t) = (3.00 m/s³)r³…

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

Q: The velocity of a particle traveling in a straight line is given by v = (6t - 3t^2) m/s, where t is…

A: Given: The velocity of a particle traveling in a straight line is given by v = (6t - 3t^2) m/s.…

Q: The velocity of particle which moves along straight line is given by V = 2 – 4t + 5t3/2 where t is…

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Q: An object has an acceleration defined by the equation a=5t+4 (m/s^2) where "t" is in seconds. The…

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Q: The velocity of a particle which moves along S-axis is given by  V=2-4t+5t^(3/2) where t is is…

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Q: If a car location is given by the relation s = 7t^2 – 2.1/(2t+1)^3, what is the acceleration of the…

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Q: If the acceleration of a particle on a straight line is given by a(t) = 2t + 1, with s(0) = 3 and…

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Q: A particle travels so that its acceleration is given by a = 2e-ti + 5 cos t j 3 sin t k If the…

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Q: An object is moving along a straight line, so that its distance x m from the origin after t seconds…

A: Given, Position of particle in time t, x = 2t3 - 15t2 + 36t

Q: The position of an object moving in a straight path is given by s(t)=5t−1 What is the…

A: The instantaneous velocity is given by, v(t)=ds(t)dt Where, s(t) is position at time t.

Q: A graph of position versus time for a certain particle moving along the x-axis is shown in the…

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Q: The motion of a particle is given by the parametric equations x=t2-3t y=t2-2t Does the particle…

A: For the particle to come to rest both x and y component of velocity should be zero at the same time.…

Q: The position of a particle in millimeters is given by s = 30 - 13t + t? where t is in seconds. Plot…

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Q: The position of a particle is described byr = (t3+ 4t –4) m and θ = (t3/2) rad, where t is…

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Q: A particle traveling in a straight line starts from rest it has an acceleration of a=B^2/3t ^2+c^2…

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Q: Where is the particle when it reaches its minimum speed (after t = 0)?

A: Given: xt = t3-3t2+6t m

Q: The position of a particle moving along thex axis is given in centimeters by x = 9.88 + 1.40 t°,…

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

Q: The position of a particle moving along the x axis is given by x=3t2-15t-10m, where t is in s.…

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Q: The acceleration of a jeepney is given by ax(t) = at - Bt^2; where a= 1.50 m/s^3 and ß = 0.120 m/s^4…

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Q: Suppose the position of an object moving in a straight line is given by s(t) = 4t² + 5t + 2. Find…

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Q: the position of particle is described by r= (t3+4t-4) mm and 0=(t3/2) rad, where t is in seconds.…

A: Given ,rt=t3+4t-4mmθt=t32rad

Projectile Motion