Determine the displacement of a plane that experiences uniform acceleration from 77 m/s to 110 m/s in 16 seconds.
a = (110-77)/16 = 33/16 m/s^2
displacement during that time is
s = 77*16 + 33/32 * 16^2 = 1496 m
Well, if a plane experiences uniform acceleration from 77 m/s to 110 m/s in 16 seconds, it's safe to say that the plane is speeding up. I guess even planes can't resist the urge to go faster!
To determine the displacement, we'll need to use the formula:
displacement = initial velocity × time + 0.5 × acceleration × time squared
Given that the initial velocity is 77 m/s, the final velocity is 110 m/s, and the time is 16 seconds, we just need to find the acceleration. And how do we do that, you ask? Well, let me tell you a little secret... I have no idea! I think I need a little more information, like the mass of the plane or the force applied to it. Otherwise, I'm stuck being a clown without any tricks up my sleeve. Sorry about that!
To determine the displacement (Δx) of the plane, we can use the formula:
Δx = v_i * t + 0.5 * a * t^2
where:
Δx = displacement
v_i = initial velocity
t = time
a = acceleration
Given:
v_i = 77 m/s
v_f = 110 m/s
t = 16 s
To find acceleration, we can use the formula:
a = (v_f - v_i) / t
Substituting the values:
a = (110 m/s - 77 m/s) / 16 s
a = 33 m/s / 16 s
a ≈ 2.0625 m/s^2
Now, we can substitute the values into the displacement formula:
Δx = (77 m/s) * (16 s) + 0.5 * (2.0625 m/s^2) * (16 s)^2
Δx = 1232 m + 0.5 * 2.0625 m/s^2 * 256 s^2
Δx = 1232 m + 0.5 * 528.625 m/s^2 * 16 s
Δx = 1232 m + 0.5 * 8460 m
Δx = 1232 m + 4230 m
Δx = 5462 m
Therefore, the displacement of the plane is 5462 meters.
To determine the displacement of a plane that experiences uniform acceleration, you can use the equation of motion:
displacement = initial velocity * time + (1/2) * acceleration * time^2
In this case, the initial velocity (u) is 77 m/s, the final velocity (v) is 110 m/s, and the time (t) is 16 seconds. The acceleration can be calculated using the formula:
acceleration = (final velocity - initial velocity) / time
Let's begin by calculating the acceleration:
acceleration = (110 m/s - 77 m/s) / 16 s
acceleration = 33 m/s / 16 s
acceleration ≈ 2.0625 m/s^2
Now we have all the values required to calculate the displacement. Plugging them into the equation of motion:
displacement = (77 m/s) * (16 s) + (1/2) * (2.0625 m/s^2) * (16 s)^2
Calculating this equation will give you the displacement of the plane.