At time t= 0, a 2150-kg spacecraft in outer space fires an engine that exerts an

Question

At  time t=  0,  a  2150-kg  spacecraft  in  outer  space  fires  an engine  that  exerts  anincreasing force on it in the +x-direction. This force obeys the equation Fx=At^2, where t is  time,  and  has  a  magnitude  of  781.25  N  when t=  1.25  s. Assume  that  the  spacecraft has zero velocity at t= 0.

(a) Find the value of the constant A, including its units.

(b) What  impulse  does  the  engine  exert  on  the  spacecraft  during  the  1.5  s  interval starting 2.0 s after the engine is fired?
(c) By how much does the spacecraft At  time t=  0,  a  2150-kg  spacecraft  in  outer  space  fires  an engine  that  exerts  anincreasing force on it in the +x-direction. This force obeys the equation Fx=At^2, where t is  time,  and  has  a  magnitude  of  781.25  N  when t=  1.25  s. Assume  that  the  spacecraft has zero velocity at t= 0.

(a) Find the value of the constant A, including its units.

(b) What  impulse  does  the  engine  exert  on  the  spacecraft  during  the  1.5  s  interval starting 2.0 s after the engine is fired?
(c) By how much does the spacecraft

Explanation / Answer

a) at t= 1.25

781.25 = A*1.25^2==================> A = 500 N/s^2

b) impulse = integration of F

P = (A/3)*(t2^3-t1^3) = (500/3) * ( 3.5^3-2^3)= 5812.5 Ns

c) impulse = change in momentum

P = m*(v-u)

v-u= P/m = 2.703 m/s

d)

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