4. -/0.85 points Tipler6 2.P.110 The acceleration of a certain rocket is given b

Question

4. -/0.85 points Tipler6 2.P.110 The acceleration of a certain rocket is given by ax - bt, where b is a positive constant. (a) Find the position function x(t) ifx-xo and vo at t = O. (Use the following as necessary: xo, vo, b, and t.) x(t) = (b) Find the position and velocity at t = 7.3 s if Xo = o, vo = o and b = 2.6 m/s x(7.3 s) = (7.3 s) (c) Compute the average velocity of the rocket between t = 6.8 s and 7.8 s at t = 7.3 s if Xo = 0, vo = o and b = 2.6 m/s.. Vavg = Is this average velocity in good agreement with the instantaneous velocity at t-7.3 s? m/s Yes No

Explanation / Answer

4)
ax = b*t
At t = 0 , x = xo , v = vo

Now,
v(t) = ax . dt
v(t) =  b*t . dt
v(t) = bt^2/2 + vo

x(t) = vt . dt
x(t) = (bt^2/2 + vo) dt
x(t) = xo + (bt^3)/6 + vo*t


(b)
At t = 7.3 s
b = 2.6 m/s^3
xo = 0,
vo = 0

x(t) = xo + (bt^3)/6 + vo*t
x(7.3) = 0 + (2.6*7.3^3)/6 + 0*t
x(7.3) =  168.6 m

v(t) = bt^2/2 + vo
v(7.3) = 2.6* 7.3^2/2 + 0
v(7.3) = 69.3 m/s


(c)
At t = 6.8 s - 7.8 s
b = 2.6 m/s^3
xo = 0,
vo = 0

x(t) = xo + (bt^3)/6 + vo*t
x(6.8) = 0 + (2.6*6.8^3)/6 + 0*t
x(6.8) =  136.25 m

x(t) = xo + (bt^3)/6 + vo*t
x(7.8) = 0 + (2.6*7.8^3)/6 + 0*t
x(7.8) =  205.6 m

Vavg = x(7.8) - x(6.8) / (7.8 - 6.8)
Vavg = (205.6 - 136.25) / 1
Vavg = 69.35 m/s

Yes the Average Velocity is in Agreement.
please post seperate questions in seperate post.

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