Answer:
176.4 meters
Explanation:
The first equation is for average velocity. The other three are the constant acceleration equations you'll need to know.
v = at + v₀
v² = v₀² + 2a(x − x₀)
x = x₀ + v₀ t + ½ at²
x is the final position
x₀ is the initial position
v is the final velocity
v₀ is the initial velocity
t is time
a is acceleration
Notice that the first equation is independent of position.
The second equation is independent of time.
The third equation is independent of final velocity.
So knowing which information you <em>don't</em> have will point you to which equation you should use.
Let's begin:
"Which one would be best to find the distance the object fell from free-fall if it fell for six seconds, assuming if fell in the absence of air resistance and it still hasn't hit the ground? Solve this problem and show all steps of work."
We want to find the distance (change in position). We're given the time (t = 6 s) and we're given the acceleration (free fall without air resistance, so a = -9.8 m/s²).
We aren't given the final velocity, so the equation we should use is the third one:
y = y₀ + v₀ t + ½ at²
Unfortunately, we aren't told the initial velocity, but if we assume that the object starts at rest, then v₀ = 0 m/s. Substituting all values:
y = y₀ + (0 m/s) (6 s) + ½ (-9.8 m/s²) (6 s)²
y − y₀ = -176.4 m
The displacement is -176.4 m. Distance is the magnitude of displacement, so we can say the object fell 176.4 meters.
