I NEED THESE FOLLOWING QUESTIONS ANSWERED & WORKED OUT. PLEASE SHOW ALL WORK!!!!

Question

I NEED THESE FOLLOWING QUESTIONS ANSWERED & WORKED OUT. PLEASE SHOW ALL WORK!!!!

1. The vector position of a particle varies in time according to the expression r = (9.00 i -9.40t^2 j) m. What is the velocity and acceleration as a function of time?

2. For the particle in the question 1 above , Determine the particle's position an velocity at t= 1.00s.

3. A particle initially located at the origin has an acceleration of a= 2.00 j m/s^2 and an initial velocity of v0=6.00 i m/s. Write the expression for vectors position and the velocity at any time t.

4. For the particle in the question 3 above, Find the position and velocity at t = 8.00 s.

5. An athlete rotates a 1.00 kg discus along a circular path of radius 3.281 ft. The maximum speed of the discus is 17.0 m/s. Determine the magnitude of the maximum radial acceleration of the discus.

6. A train slows down as it rounds a sharp horizontal turn, slowing with a constant tangential acceleration from 98.7 km/h in the 16.5 s that it takes to round the bend. The radius of the curve is 149 m. compute the magnitude acceleration at the moment the train speed reaches 46.5 km/h. Assume that it continues to slow down at this time at the same rate.

Explanation / Answer

Here ,

1)

r = 9 i - 9.40 t^2

velocity of the particle =dr/dt

velocity of the particle = d/dt(9 i - 9.40 t^2)

velocity of the particle = - 18.8 t j m/s

acceleration = -dv/dt

acceleration = -18.8 j m/s^2

2)

for the time ,t = 1 s

position = 9 i - 9.4 * 1^2 j

position = 9 i - 9.4 j m

velocity = -18.8 * 1 j m/s

velocity = -18.8 j m/s

3)

a = 2 j m/s^2

v0 = 6 i m/s

for the velocity vector

v = 6 i + integration(a .dt)

v = 6i + 2t j m/s

for the position vector

r = integration(6i + 2t j m/s)

r = 6 t i + t^2 j

4) at t = 8 s

v = 6 i + 2 * 8 j

v = 6 i + 16 j

the velocity at t = 8 s is 6 i + 16 j

for the position ,

r = 6 * 8 i + 8^2 j

r = 48 i + 64 j m

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