A supersonic jet flying at 137 m/s is accelerated uniformly at the rate of 23.1 m/s2 for 20.0 s.
(a) What is its final velocity?
(b) The speed of sound in air is 331 m/s. How many times the speed of sound is the plane's final speed?
(a) To find the final velocity, we can use the formula:
Final velocity = initial velocity + (acceleration × time)
Final velocity = 137 m/s + (23.1 m/s² × 20.0 s)
Final velocity = 137 m/s + 462 m/s
Final velocity = 599 m/s
The final velocity of the jet is 599 m/s.
(b) To find how many times the speed of sound the final speed is, we can divide the final speed by the speed of sound:
Number of times the speed of sound = final speed / speed of sound
Number of times the speed of sound = 599 m/s / 331 m/s
Number of times the speed of sound ≈ 1.81
The plane's final speed is approximately 1.81 times the speed of sound.
To find the final velocity of the jet, we can use the equation:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Given:
u = 137 m/s (initial velocity)
a = 23.1 m/s² (acceleration)
t = 20.0 s (time)
(a) Using the equation, we can substitute the given values to find the final velocity:
v = 137 m/s + (23.1 m/s²)(20 s)
v = 137 m/s + 462 m/s
v = 599 m/s
Therefore, the final velocity of the jet is 599 m/s.
(b) To find how many times the speed of sound the plane's final speed is, we can divide the final speed of the jet by the speed of sound:
Number of times = final speed / speed of sound
final speed = 599 m/s
speed of sound = 331 m/s
Number of times = 599 m/s / 331 m/s
Number of times = 1.81
Therefore, the plane's final speed is approximately 1.81 times the speed of sound.
To find the answers to these questions, we need to apply the basic equations of kinematics.
The equation for final velocity (v) can be found using the formula:
v = initial velocity (u) + acceleration (a) * time (t)
For the first question, we can plug in the given values:
u = 137 m/s (initial velocity)
a = 23.1 m/s^2 (acceleration)
t = 20.0 s (time)
Using the formula, we can calculate the final velocity (v) as follows:
v = 137 m/s + (23.1 m/s^2) * (20.0 s)
v = 137 m/s + 462 m/s^2 * s
v = 137 m/s + 4620 m/s
v = 4757 m/s
Therefore, the final velocity of the jet is 4757 m/s.
For the second question, we can find the ratio of the final velocity of the jet to the speed of sound in air.
The ratio is calculated as:
Final speed of the jet / Speed of sound in air
Let's substitute the values:
4757 m/s / 331 m/s
Simplifying, we find:
= 14.37
Therefore, the final speed of the jet is approximately 14.37 times the speed of sound in air.