physics question

Question

An airplane starts from rest and accelerates at a constant 3.00 m/s² for 20.0 s. What is its displacement in this time? Use physics symbols to label

Answer 1

For this question, you'll need to use the following kinematics equation for constant acceleration:

x = x₀ + v₀t + 1/2 at²

where x is position, v is velocity, a is acceleration, and t is time. The "₀" subscript on x and v, pronounced "nought," means "initial."

So we just need to plug in the values from the problem. Since the airplane starts from rest, the initial velocity is 0:

v₀ = 0 m/s

a = 3.00 m/s²

t = 20.0 s

Since displacement, sometimes indicated as "Δx", is the difference between the final position and the initial position, we can rearrange the equation as:

Δx = x – x₀ = v₀t + 1/2 at²

Δx = v₀t + 1/2 at² = (0)(20.0 s) + 1/2 (3.00 m/s²)(20.0 s)²

Make sure to keep track of your units as you go:

Δx = (1/2 × 3.00 × 20.0²) (m/s² × s²)

= 600. m

So, the displacement of a plane starting from rest in 20.0 s at a constant acceleration of 3.00 m/s² is 600. m.

P.S. Be sure to retain the correct number of significant figures: in this case, three, since both given values (3.00 and 20.0) have 3 significant figures. The decimal at the end of 600 indicates that the 6, the 0 in the tens place, and the 0 in the ones place are all significant digits, and the answer is accurate within 1 or 2 meters. If we just write "600," we might mean that only 6 is a sig fig, and that the answer has a much greater uncertainty in the realm of ±100 meters.

Answer 2

Hi Gin! First, we need to assume that the plane is traveling in a straight line, or else the question is unanswerable as is.

One approach is to find the average speed of the plane, and then multiply by the total time until we measure displacement(20 seconds). Average speed is pretty straight forward: since acceleration is uniform, just take the initial speed(0) and the final speed(3.00m/s² * 20s = 60 m/s) and divide by two, for an average speed of (0m/s + 60 m/s)/2 = 30 m/s. Displacement is just equal to the average speed * time traveled, which in this case, is 30m/s * 20s = 600 meters.