A drag racer, starting from rest, speeds up for 384 m with an acceleration of +19.3 m/s2. A parachute then opens, slowing the car down with an acceleration of -6.33 m/s2. How fast is the racer moving 302 m after the parachute opens?

To solve this problem, we can break it down into three parts:

1. Calculate the final velocity of the car after the acceleration phase.
2. Calculate the time it takes for the car to reach the parachute opening point.
3. Use the final velocity and the time to calculate the velocity 302 m after the parachute opens.

Let's start with Step 1:

1. Calculate the final velocity of the car after the acceleration phase.

We can use the equation of motion:
v^2 = u^2 + 2as

where:
v = final velocity
u = initial velocity (which is 0 m/s because the car starts from rest)
a = acceleration
s = distance traveled (384 m)

Plugging in the given values:
v^2 = 0^2 + 2 * 19.3 m/s^2 * 384 m
v^2 = 0 + 2 * 19.3 m/s^2 * 384 m
v^2 = 14822.4 m^2/s^2

Taking the square root of both sides:
v = √(14822.4 m^2/s^2)
v ≈ 121.6 m/s

So the final velocity after the acceleration phase is approximately 121.6 m/s.

Moving on to Step 2:

2. Calculate the time it takes for the car to reach the parachute opening point.

We can use the equation of motion:
v = u + at

where:
v = final velocity after acceleration phase (121.6 m/s)
u = initial velocity (0 m/s)
a = acceleration during the parachute phase (-6.33 m/s^2)
t = time

Plugging in the given values:
121.6 m/s = 0 m/s + (-6.33 m/s^2) * t
121.6 m/s = -6.33 m/s^2 * t

Solving for t:
t = 121.6 m/s / -6.33 m/s^2
t ≈ -19.20 s (Note: The negative sign indicates that deceleration is taking place.)

It takes approximately 19.20 seconds for the car to reach the parachute opening point.

Finally, moving on to Step 3:

3. Calculate the velocity 302 m after the parachute opens.

We can use the equation of motion:
v = u + at

where:
v = final velocity 302 m after the parachute opens (the value we want to find)
u = velocity after acceleration phase (121.6 m/s)
a = acceleration during the parachute phase (-6.33 m/s^2)
t = time (19.20 s)

Plugging in the given values:
v = 121.6 m/s + (-6.33 m/s^2) * 19.20 s
v = 121.6 m/s - 121.536 m/s
v ≈ 0.064 m/s

Therefore, the racer is moving approximately 0.064 m/s 302 m after the parachute opens.