Find the displacement of a particle moving in a straight line with velocity v(t) = 50t – 3 m/s over the time interval [3, 7]. (Give your answer as a whole or exact number.) displacement:

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Q: A particle moves along the x-axis so that at time t > 0 its position is given by x(t) = t – 24t.…

A: This is an application of differential calculus.

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Q: 10. On July 2, 2019, a total solar eclipse will occur over the South Pacific Ocean and parts of…

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Q: i dont understand a) through d)

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Q: a) When is the particle at rest? b) During what time interval is the particle moving right? Left?…

A: (a) The particle is at rest when velocity is zero. And we know velocity V(t) is the derivative of…

Q: 3. A tiny organism begins to move in a straight line with velocity v(t) = t(t – 1)'/3 microns per…

A: Let the expression for the velocity is v(t)=t(t2-1)1/3. Integrate the expression to find the…

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: A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is…

A: Given a(t)=cos t Integrating with respect to t to get velocity function, vt=∫atdtvt=∫cos t…

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A: The detailed solution is given below  Thank you

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;…

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Q: Find the total distance traveled by a particle according to the velocity function v(t)=−t+7 m/sec…

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Q: The position of a particle at time tis s(t) = 2t 3• Compute the average velocity over the time…

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Q: 8. At noon a car starts from rest at point A and proceeds with constant acceleration along a…

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Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = 3t2 – 60t.…

A: v(t)=3t2-60t,    t≥0the particle is moving to the right whenv(t)>03t2-60t>03t(t-20)>0

Q: Let r(t) be the rate at which the world’s oil is consumed,where is measured in years starting at t…

A: Given: Let r(t) be the rate at which the world’s oil is consumed,where is measured in years starting…

Q: 2. A particle starting with velocity u is falling freely under gravity with a constant acceleration.…

A: Introduction :

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Q: A particle moves in a straight line from the origin (at t= 0) with given initial velocity u, and…

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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: A stone is tossed in the air from ground level with an initial velocity of 15 m/s. Its height at…

A: Average velocity is given by: Avg. Velocity=Final position - Initial PositionTime taken We have,…

Q: The equation for the amount Q of an antibiotic in the bloodstream at time t is Q = Ae-kt. %3D dQ 1.…

A: Q=Ae-kt Q is the amount of antibiotic in the bloodstream at time t Now we take derivative at time t…

Q: Given the acceleration of an object and its initial velocity, how doyou find the velocity of the…

A: We know that the rate of change of velocity of a moving particle is known as its acceleration. Let…

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Q: A stone is tossed vertically into the air from ground level with an initial velocity of 15 mis. Its…

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

A: Given:

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Q: Ithe particle is at the point (1, ) at time t 0, how far is the particle from the origin at time t=…

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Q: Find the displacement of a particle moving in a straight line with velocity v(t) = 16t – 8 m/s over…

A: Topic = Application of integration

Q: A particle initially situated at the origin moves along the x-axis so that its acceleration at any…

A: Integrate the expression a(t)=2t-7 to find the velocity of the particle.…

Q: A particle moves along the X-axis so that at time t>0 its position is given by x(t)= 2t3 +…

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

A: St=t4-18t2The particle passes through the origin when St=0t4-18t2=0t2t2-18=0t2=0   t2-18=0⇒t=0…

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: A parachutist of mass 67.4 kg jumps out of a stationary hot air balloon. Use Eq. (1.10): (t) = (1-…

A: Given : v(t)=gmc(1-e-(c/m)t)Gravitational acceleration g=9.81 m/s2Mass m=67.4 KgDrag coefficient…

Q: body mass 4 kg falls(at rest) from a medium whose resisting force is numerically equal to 0.003v,…

A: Topic:- Basic maths