A particle moves along a line with velocity function ?(?) = ?^2 − ?, where v...

A particle moves along a line with velocity function ?(?) = ?^2 − ?, where v is measured in meters per second. a. Find distance traveled by the particle in time interval [0, 6] seconds. b. Find the net displacement. 8. Estimate the area from -1 to 9 under the graph of f(x) = 81 – x^2 using five approximating rectangles and midpoints as sample points.

Expert Solution

milcah answered 2 years ago

Particle A moves along an axis in the laboratory with velocity V = 0.3c. Particle b...

Particle A moves along an axis in the laboratory with velocity V = 0.3c. Particle b moves with velocity of V = .9c along the direction of motion of particle A. What kinetic energy does the particle b measure for the particle A?

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]?

A particle moves along a straight line with an acceleration a=2v1/2m/s2, where v is in m/s....

A particle moves along a straight line with an acceleration a=2v1/2m/s2, where v is in m/s. If s = 0, v = 1 m/s when t = 0, determine the time for the particle to achieve a velocity of 18 m/s. Also, find the displacement of particle when t = 1 s. Express your answer using three significant figures and include the appropriate units.

2. a. A particle moves in a straight line along with the ? − ???? its...

2. a. A particle moves in a straight line along with the ? − ???? its displacement is given by the equation ?(?) = 5? 3 − 8? 2 + 12? + 6,? ≥ 0, where ? is measured in seconds and s is measured in meters. Find: i. The velocity function of the particle at time ? (2marks) ii. The acceleration function of the particle at time t. (2marks) iii. The acceleration after 5 seconds (1marks) b. Find the...

A particle moves with acceleration function a(t) = 2x+3. Its initial velocity is v(0) = 2...

A particle moves with acceleration function a(t) = 2x+3. Its initial velocity is v(0) = 2 m/s and its initial displacement is s(0) = 5 m. Find its position after t seconds.

Suppose a particle moves along a line according to the motion function f(t) = 9/t+9, where...

Suppose a particle moves along a line according to the motion function f(t) = 9/t+9, where t is measured in seconds and f(t) is measured in feet. Use this motion function to answer the following questions: a.) What is the initial velocity of the particle? b.) When is the particle at rest? c.) When is the particle moving in the negative direction?

A 1.90-kg particle moves in the xy plane with a velocity of v with arrow =...

A 1.90-kg particle moves in the xy plane with a velocity of v with arrow = (4.00 i − 3.70 j) m/s. Determine the angular momentum of the particle about the origin when its position vector is r with arrow = (1.50 i + 2.20 j) m.

A particle with positive charge q = 9.61 10-19 C moves with a velocity v =...

A particle with positive charge q = 9.61 10-19 C moves with a velocity v = (3î + 4ĵ − k) m/s through a region where both a uniform magnetic field and a uniform electric field exist. (a) Calculate the total force on the moving particle, taking B = (4î + 3ĵ + k) T and E = (3î − ĵ − 4k) V/m. (Give your answers in N for each component.) Fx = N Fy = N Fz =...

A particle of mass M moves along a straight line with initial speed vi. A force...

A particle of mass M moves along a straight line with initial speed vi. A force of magnitude Fpushes the particle a distance D along the direction of its motion. A) Find vf, the final speed of the particle after it has traveled a distance D. Express the final speed in terms of vi, M, F, and D. B) By what multiplicative factor RK does the initial kinetic energy increase, and by what multiplicative factor RW does the work done...

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