Problem Your school science club has devised a special event

Problem: Your school science club has devised a special event for homecoming. You\'ve attached a rocket to the rear of a small car that has been decorated in the blue-and-gold school colors. The rocket provides a constant acceleration for 9.0s. As the rocket shuts off, a parachute opens and slows the car at a rate of 5.0m/s2. The car passes the judges\' box in the center of the grandstand, 990mfrom the starting line, exactly 12s after you fire the rocket.

1.) What is the car\'s speed as it passes the judges?

Please write out each step with explanation. Thank you so much

Solution

1) Suppose acceleration provided by rocket is a.

then ,

distance traveled in 9s.

d = u t + a t^2 /2

d1 = 0 + a 9^2 /2 = 40.5a

velocity after 9sec,

v1 = 9 a { v =u + at}

now a = - 5 m/s^2

distance traveled in 3 sec after 9sec,

d2 = (9a) (3) + (-5)(3^2)/2 = 27a - 22.5

and d1 + d2 = 990

40.5a + 27a - 22.5 = 990

a = 15 m/s^2

Speed at t = 9s ,

v = 0 + (15x 9) = 135 m/s

then after 3sec (at t = 12s)

v = 135 - (3 x 5) = 120 m/s ...............Ans