1. Suppose the velocity of a moving object is given by the function f(t) = √...

1. Suppose the velocity of a moving object is given by the function f(t) = √ t for the time interval 0 ≤ t ≤ 2 sec. Approximate the total distance this object travels during this entire time interval with:

(a) (4 pts) a Left-Hand Riemann sum using n = 4 rectangles. Write out the terms in the sum, but DO NOT evaluate it.

(b) (4 pts) a Right-Hand Riemann sum using n = 6 rectangles. Write out the terms in the sum, but DO NOT evaluate it.

(c) (2 pts) Draw a sketch of y = √ x to determine which sum is an overestimate of the total distance traveled during the given time interval (circle one choice). Your sketch should justify how you made your choice. • the Left-Hand Riemann sum • the Right-Hand Riemann sum • neither

Expert Solution

milcah answered 2 years ago

The function sequals=?f(t) gives the position of an object moving along the? s-axis as a function...

The function sequals=?f(t) gives the position of an object moving along the? s-axis as a function of time t. Graph f together with the velocity function ?v(t)equals=StartFraction ds Over dt EndFractiondsdtequals=f prime left parenthesis t right parenthesisf?(t) and the acceleration function ?a(t)equals=StartFraction d squared s Over dt squared EndFractiond2sdt2equals=f prime prime left parenthesis t right parenthesisf??(t)?, then complete parts? (a) through? (f). sequals=112112tminus?16 t squared16t2?, 0less than or equals?tless than or equals?77 ?(a heavy object fired straight up from? Earth's...

The velocity function of a particle moving along a line is given by the equation v(t)...

The velocity function of a particle moving along a line is given by the equation v(t) = t2 - 2t -3. The particle has initial position s(0) = 4. a. Find the displacement function b. Find the displacement traveled between t = 2 and t = 4 c. Find when the particle is moving forwards and when it moves backwards d. Find the total distance traveled between t = 2 and t = 4 e. Find the acceleration function, and...

The velocity function for a particle moving along a straight line is given by v(t) =...

The velocity function for a particle moving along a straight line is given by v(t) = 2 − 0.3t for 0 ≤ t ≤ 10, where t is in seconds and v in meters/second. The particle starts at the origin. (a) Find the position and acceleration functions for this particle. (b) After ten seconds, how far is the particle from its starting point? (c) What is the total distance travelled by the particle in the interval [0, 10]?

The position function of an object moving along a straight line is given by the function...

The position function of an object moving along a straight line is given by the function t3 - 15t2 -48t -10, where s is in metres and t is in seconds and 0≤15≤t . [7A] a) When is the velocity of the object greater than 21 m/s? b) When is the speed of the object less than 21 m/s? c) Illustrate the graphical representation for each of the above."

(c++) the constant velocity of an object moving in straight line is defined as r= d/t,...

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The position vector F(t) of a moving particle at time t[s] is given by F(t)= e^t...

The position vector F(t) of a moving particle at time t[s] is given by F(t)= e^t sin(t)i-j+e^t cos(t)k a) Calculate the acceleration a(t). b) Find the distance traveled by the particle at time t = 3π/2, if the particle starts its motion at time t = π/2. c) Find the unit tangent vector of this particle at time t = 3π/2. d) Find the curvature of the path of this particle at time t = 3π/2.

An object with a mass of 49.8 pounds is moving with a uniform velocity of 30.9...

An object with a mass of 49.8 pounds is moving with a uniform velocity of 30.9 miles per hour. Calculate the kinetic energy of this object in joules

1) The position of an object moving along a straight line is s(t) = t^3 −...

1) The position of an object moving along a straight line is s(t) = t^3 − 15t^2 + 72t feet after t seconds. Find the object's velocity and acceleration after 9 seconds. 2) Given the function f (x ) =−3 x 2 + x − 8 , (a) Find the equation of the line tangent to f(x ) at the point (2, −2) . (b) Find the equation of the line normal to f(x ) at the point (2, −2)...

f(t) = 1- t 0<t<1 a function f(t) defined on an interval 0 < t <...

f(t) = 1- t 0<t<1 a function f(t) defined on an interval 0 < t < L is given. Find the Fourier cosine and sine series of f and sketch the graphs of the two extensions of f to which these two series converge

1) Imagine an object moving horizontally with uniform (that is, constant) velocity. Sketch the position time...

1) Imagine an object moving horizontally with uniform (that is, constant) velocity. Sketch the position time and velocity-time graphs for this motion. 2) Imagine tossing an object straight up into the air, then catching it. Sketch the position-time and velocity-time graphs for this motion, from the moment it leaves your hand to the moment just before it lands in your hand. 3) Imagine tossing a ball slightly upwards and towards another person. Consider the motion from the moment the ball...

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