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, 990m from the starting line, exactly 12s after you fire the rocket. Part A What is the car's speed as it passes the judges

Explanation:

Acceleration acts for 9 s and deceleration acts for 12 - 9 = 3 s.

Total distance covered = 990 m

initial velocity u = o

Distance covered while accelerating

s₁ = 1/2 a 9² where a is the acceleration

= 40.5 a

final velocity after 9 s

v = at = 9a

while decelerating

v² = u² - 5 x s₂

0 = (9a)² - 5 s₂

s₂ = 16.2 a²

Distance covered while decelerating = 16.2 a²

s₁ + s₂ = 990

40.5 a + 16.2 a² = 990

16.2 a² + 40.5 a - 990 = 0

a = 6.5

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