A supersonic jet flying at +145 m/s experiences uniform acceleration at the rate of +23.1 m/s2 for 20.0 s.

Question

a. What is its final velocity?
b. The speed of sound is 331 m/s in air. What is the plane's speed in terms of the speed of sound?

Answer 1

a. To find the final velocity (v final), we can use the formula:

v final = v initial + a * t

where:
v initial is the initial velocity of the jet (145 m/s),
a is the acceleration of the jet (23.1 m/s²), and
t is the time interval (20.0 s).

v final = 145 m/s + 23.1 m/s² * 20.0 s
v final = 145 m/s + 462 m/s²
v final = 607 m/s

Therefore, the final velocity of the jet is 607 m/s.

b. We can compare the speed of the plane (v plane) to the speed of sound (v sound) using the formula:

v plane = m * v sound

where:
m is a dimensionless constant representing the ratio of the speed of the plane to the speed of sound.

By rearranging the formula, we can express the ratio (m) as:

m = v plane / v sound

Substituting the given values, we have:

m = 607 m/s / 331 m/s
m ≈ 1.834

Therefore, the plane's speed is approximately 1.834 times the speed of sound.