d's = 30 Vt- ds ds A particle moves on a coordinate line with acceleration subject to the conditions that = 6 and s = 11 when t = 1. Find the velocity v = dt dt dt? terms of t and the position s in terms of t.

Q: A particle moves on a coordinate line with acceleration dt? = 60 f - 18 subject to the ds = 8 and s…

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Q: A particle moves with position function s(t) = t – 4t³-20t?+20t where t > 0. At what time does the…

A: This question is based on application of Derivative.

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Q: Determine the speed dt ds at time t. (Assume units of meters and seconds.) (3t°, 2t2), t = 4 ds m/s…

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Q: 6. A particle moves with position function S(t) = – 2? + 31, t0 [T:3] a) Determine the velocity of…

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Q: A particle moves along a coordinate axis. Its position at time tis given by s(t) = t – 9t² + 24t +…

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Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t2…

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Q: give the acceleration a = d2s/dt2, initial velocity,and initial position of an object moving on a…

A: We know that velocity, y=dsdt and acceleration, a=dydt. We have given a=-4sin 2t. To find velocity y…

Q: A particle is moving with acceleration a(t) = 18t + 8 82 Its position at time t = 0 seconds is s(0)…

A: Consider the given acceleration of the moving particle at=18 t+8  First, find the velocity of the…

Q: dy (a) If y = e° sin-1 (0) and z = e28 + cos-1 (0), find dx (b)Find the equations of the tangent and…

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Q: e3x d 6. (10) Calculate dx cot(t)dt. 2

A: Solve by using substitution and first solve the integral and then go for differentiation. Do step by…

Q: Using a(t) = (d2s/dt2) = -4 sin 2t, v(0) = 2, s(0) = -3 find the body's position at time t.

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Q: v(t)is the velocity of a moving object measured in feet per minute. (a) What does v(t) dt represent?…

A: 14. Given that, vt is the velocity of a moving object measured in feet per minute. (a) From the…

Q: Beginning at t = 0 s with initial velocity 4 m/s, a particle moves in a straight line with…

A: Initial velocity of particle = u = 4 m/saccelerationof particle = a = 3t m/s2time taken by the…

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t2…

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Q: A particle is moving with acceleration a(t)= 18t+4 its position at time t= 0 is s(0) = 5 and its…

A: Given query is to find the position of the partical at t = 4.

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t2…

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Q: . A particle moving in space has a position at any time t, given by «(t) = (2t° + 1)i + ti-(+3¢)k at…

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Q: Find the position of a body moving on a coordinate line at time t for an acceleration a = d's - = 4…

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Q: A particle is moving on a straight line has acceleration a=5-3t and it's velocity at time=2. If s(t)…

A: Solution: a = 5-3t v(2)=7 s(2) - s(1)=?

Q: d?s = 8 e 2t, initial velocity v(0) = 10, and initial position s(0) = 5. Find the position of a body…

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Q: Alma observes an object moving in a straight line with an initial velocity of – 10 m/s undergoes an…

A: Given: at=12t-8 ms2 We know that for given acceleration functionat, velocity functionvt and position…

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A: Given To find the velocity at time ‘t’ , take the integral of a(t)

Q: The velocity function of a particle moving along a line is   v(t) = 3·t2 − 12·t + 9, where t is in…

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Q: At time t, the position of a body moving along the s-axis is s=3- 212 + 120t m. Find the body's…

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Q: v(4) = V21 S a(4) = 21 Find the velocity and the acceleration at time t = 4 s for the position…

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Q: The velocity of a particle moving in the plane has components dx = 12t – 312 and- dt dy = In(1 + (t…

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Q: Q2) the velocity (V = ) and initial position of a body moving along a dt coordinates line , Find the…

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Q: ds The position of a particle at time t is given by s. Find the velocity dt s4-7st+2t-3t= 0 ds dt

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Q: A weather balloon is released and rises vertically such that its velocity for the first 10 seconds…

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Q: ds The velocity of a particle moving back and forth on a line is v = = 6 sin(2t) m/sec for dt all t.…

A: Given:   To find:

Q: 5. A heavy rock blown straight up from the ground by a dynamite blast. The velocity time t during…

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Q: Two particles have positions at time t seconds given by the t3 -t meters and s2 equations s1 61² –…

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Q: A particle moves along a coordinate axis. Its position at time t is given by s(t) = t² - 5t + 1, t >…

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Q: A particle moves in a straight line from the origin (at t = Q) with given initial velocity vo and…

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Q: An object moves along the x-axis with its position measured relative to the origin so that its…

A: Recall what Newton had said to all of us: acceleration = a(t) = Rate of change of velocity v(t) =…

Q: 1 and t Explain and discuss the difference in velocity at times t v(t) = 2t – 1. 5 for

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Q: A particle is moving with acceleration a(t) 30t + 16. its O is s(0) = 9 and its velocity at time =…

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Q: 03. The acceleration of a particle moving along the r-axis is given by a(t) = (t – 8)sin t for 0SIS…

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Q: (8) A particle is thrown vertically upwards in the air. The distance it covers in time t i gi =(t) =…

A: Here it is given that,  the distance covers in time t is  given by, s(t)=ut-12gt2…

Q: A particle is moving with acceleration a(t) = 30t + 2. its position at time t = 0 is s(0) = 3 and…

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Q: A particle moves on a coordinate line with acceleration a = d2s/dt2 = 15√t - (3/√t), subject to the…

A: Given that, a=d2sdt2=15t-3t

Q: [2 Marks ] B2 (b): The position of a hummingbird flying along a straight line in t seconds is given…

A: We know that the acceleration is given by the second derivative of the position function. Therefore…

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t2…

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Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t2…

A: Given , velocity function  ,  v(t) = t2 - 2t -15

Q: 2. The position of a particle is i (t) = (2.0or² i+ 6.0j – 6.0t k) m. a. Determine its velocity and…

A: To find Velocity and acceleration vectors from the given position vectors.