The propulsion system on a 1500kg rocket car fires for 15 seconds and the propul
ID: 3900381 • Letter: T
Question
The propulsion system on a 1500kg rocket car fires for 15 seconds and the propulsion force is equal to F= x(80-x). This force can only act for a specific distance down the road. Suppose the car is moving at 5m/s before the rocket ignites and the car travels straight along a road. After the propulsion ceases, the car travels for another 30 seconds, assume all dissipative forces are negligible during this segment.
a. What is the final speed of the car when the propulsion ceases?
b. What is the average speed for the entire two stage event?
please explain. Thank you!
Explanation / Answer
a)F= x(80-x) = m*a
80*x-x^2=m*a
integrating wrt to time
40*x^2-x^3/3 = m*V
x=0 to x=15 sec
and Vf=?
Vi=5 ms
m=1500
substituing in above equation for definate integral values
4500-1125=m (vf-5)
vf=7.75 m/s
b)average velocity in propulsion state=inter(f(x)dx ) / x2-x1
= 6.04
total avergae 6.04+7.75 / 2 = 6.895 m/s
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