a pilot stops a plane in 484 m using a constant acceleration of -8.0 m/s^2 . How fast was the plane moving before braking began ?
To find the initial speed of the plane before braking, we can use the following equation of motion:
v^2 = u^2 + 2as
where:
- v is the final velocity (which is 0 m/s since the plane stops)
- u is the initial velocity (what we want to find)
- a is the constant acceleration of -8.0 m/s^2
- s is the distance traveled, which is 484 m
Rearranging the equation, we have:
u^2 = v^2 - 2as
Substituting the known values, we have:
u^2 = 0^2 - 2(-8.0 m/s^2)(484 m)
Simplifying the equation:
u^2 = 0 - 7744 m^2/s^2
Taking the square root of both sides to find u:
u = √(-7744 m^2/s^2)
However, we encounter an issue here. The square root of a negative number is not a real number, as the result would involve imaginary numbers. This tells us that it's not physically possible for the plane to stop within 484 m with a constant acceleration of -8.0 m/s^2.
Hence, the given scenario is not feasible, and we cannot determine the initial speed of the plane before braking began.
To determine the initial velocity of the plane before braking began, we can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s as the plane comes to a stop)
u = initial velocity (what we need to find)
a = acceleration (-8.0 m/s^2)
s = distance traveled during braking (484 m)
Plugging in the values into the equation, we have:
0^2 = u^2 + 2(-8.0 m/s^2)(484 m)
Simplifying the equation, we get:
0 = u^2 - 7744 m^2/s^2
Rearranging the equation, we have:
u^2 = 7744 m^2/s^2
Taking the square root of both sides, we find:
u = √7744 m/s
Calculating the square root, we get:
u ≈ 88 m/s
Therefore, the plane was moving at approximately 88 m/s before braking began.