Answer :
Answer:
Explanation:
Given ,
dv / dt = k ( 160 - v )
dv / ( 160 - v ) = kdt
ln ( 160 - v ) = kt + c , where c is a constant
when t = 0 , v = 0
Putting the values , we have
c = ln 160
ln ( 160 - v ) = kt + ln 160
ln ( 160 - v / 160 ) = kt
(160 - v ) / 160 = [tex]e^{kt}[/tex]
1 - v / 160 = [tex]e^{kt }[/tex]
v / 160 = 1 - [tex]e^{kt }[/tex]
v = 160 ( 1 - [tex]e^{kt }[/tex] )
differentiating ,
dv / dt = - 160k [tex]e^{kt }[/tex]
acceleration a = - 160k [tex]e^{kt }[/tex]
given when t = 0 , a = 280
280 = - 160 k
k = - 175
a = - 160 x - 175 [tex]e^{kt}[/tex]
a = 28000 [tex]e^{kt}[/tex]
when a = 128 t = ?
128 = 28000 [tex]e^{kt}[/tex]
[tex]e^{kt }[/tex] = .00457
Acceleration of a rocket model.
As acceleration is the change in the magnitude and direction of the moving body and refers to the increase in the velocity which varies over time. The acceleration of the model rocket is proportional to the r difference between the 160 feet/sec.
Thus the answer is 0.0457
- The initial velocity of the rockset at the rest and the initial acceleration is about 280 fett/ sec then the length of acceleration for the rokst to reach 128 feet / sec. Will be calculated by the dv / dt = k ( 160 - v ).
- ln ( 160 - v ) = kt + c , where c is a constant, when t = 0 , v = 0 then putting the values , we have c = ln 160
- ln ( 160 - v ) = kt + ln 160, ln ( 160 - v / 160 ) = kt
- (160 - v ) / 160 = 1 - v / 160 = v / 160 = 1 - v = 160 ( 1 - ) acceleration a = - 160k given when t = 0 , a = 280 The 280 = - 160 k, k = - 175 a = - 160 x - 175 Hence a = 2800
- Thus 128 = 28000 = .00457.
Learn more about acceleration.
brainly.com/question/13137118.