The position of the plane as it ascends is given by r=[3ati-btj-(5d-ct)k]m, where a=2.50m/s, d=1.00km, b=0.050m/s, and c=75m/s. (a) What is the position, velocity, and acceleration of the plane at t= 0?

(b) What is the position, velocity, and acceleration of the plane at t= 30.0s?

(c)What is the average velocity of the
plane between t1= 0 and t2= 30.0s?

(d) What is the average acceleration of the plane between t1= 0 and t2= 30.0s?

Explanation:

r = 3(2.50)ti - 0.050tj - (5(1000) - 75t)k m

r = 7.5ti - 0.050tj + (75t - 5000)k

a) r(0) = (0i, 0j, -5000k) m

   v(0) = r'(0) = (7.5i, -0.050j, 75k)

   a(0) = v'(0) = (0i, 0j, 0k)

b) r(30) = (225i, -1.5j, -2,750k) m

   v(30) = (7.5i, -0.050j, 75k)

   a(30) = (0i, 0j, 0k)

c) As velocity is not a function of time,

   v(avg) = (7.5i, -0.050j, 75k)

d) As acceleration is not a function of time

   a(avg) = (0i, 0j, 0k)

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explanation:

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