a plane travels 5.0x10^2 m while being accelerated uniformly from rest at the rate of 5.0m/s^2. What final velocity does it attain?
Vf^2 = Vo^2 + 2ad.
Vf^2 = 0 + 2*5*500 = 5000,
Vf = 70.71m/s.
Well, if the plane is accelerating at a rate of 5.0 m/s^2 and travels a distance of 5.0x10^2 m, it's safe to say that it's in a hurry to reach its destination!
To find the final velocity, we can use the equation:
v^2 = u^2 + 2as
Where:
v = final velocity
u = initial velocity (which in this case is 0 since the plane starts from rest)
a = acceleration
s = distance traveled
Plugging in the values, we get:
v^2 = 0 + 2(5.0 m/s^2)(5.0x10^2 m)
v^2 = 0 + 5000 m^2/s^2
So, the final velocity squared is 5000 m^2/s^2. But as much as I'd love to see a plane with a squared velocity, we need the actual velocity, so let's take the square root:
v = √5000 m^2/s^2
v ≈ 70.7 m/s
Voila! The plane attains a final velocity of approximately 70.7 m/s. Just remember to fasten your seatbelt if you're on board!
To find the final velocity attained by the plane, we can use the equation of motion:
v² = u² + 2as
Where:
v: final velocity
u: initial velocity (which is 0 in this case because it starts from rest)
a: acceleration
s: displacement
Now let's plug in the given values into the equation:
v² = 0² + 2(5.0 m/s²)(5.0×10² m)
v² = 2(5.0 m/s²)(5.0×10² m)
v² = 2(25.0 m²/s²)(10² m)
v² = 2(2500 m³/s²)
v² = 5000 m³/s²
Taking the square root of both sides to solve for v:
v = √(5000 m³/s²)
v ≈ 70.71 m/s
Therefore, the final velocity attained by the plane is approximately 70.71 m/s.