1. The vector position of a particle varies in time according to the expression

Question

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 abovre, Find the position and velocity at t=8.00s.

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.

Explanation / Answer

r = (9.00 i - 9.40t^2 j) m
v = dr/dt = -18.8t j m/s
a = dv/dt = -18.8 j m/s^2

2. at t = 1.00 s
r = (9.00 i - 9.40*1.00^2 j) m = 0.4 m
v = -18.8*1.00 j m/s = -18.8 j m/s

3.  v = u + a dt
v = 6i + 2t j
(a) the vector position ;
r = ro + v dt
= 0 + 6t i + t^2 j m
= 6t i + t^2 j m

4) v = 6i + 2t j m/s

(c) r(8) = 48i + 64j m

(d) v(8) = 6i+ 16j
l vl = sqrt ( 6^2 + 16^2) = 17.08 m/s

5). maximal radial acceleration of the discus
= v^2/r
= 17 ^2 / 1 mt
= 289 m/s^2 --answer

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