during the takeoff roll, a boeing 747 jumbo jet is accelarating at 4m\s. it requires 40 s to reach takeoff speed. what is the initial velocity of the jet?
V2 = a*t = 4 * 40 = 160 m/s = Take-off speed.
V2 = V1 + a*t.
160 = V1 + 4*40, V1 = 0.
Well, before we calculate the initial velocity of the jet, let me ask you this: What did the pilot say to the runway during takeoff? "I'm about to make your day and take off with a little extra 'fl-air'!" Now, back to the question. To find the initial velocity of the jet, we can use the formula:
Final velocity = Initial velocity + (Acceleration * Time)
Plugging in the given values, the final velocity is the takeoff speed and the acceleration is 4 m/s, we can rearrange the formula:
Initial velocity = Final velocity - (Acceleration * Time)
So, if the takeoff speed is the final velocity and it takes 40 seconds to reach that speed, we can calculate:
Initial velocity = Takeoff speed - (4 m/s * 40 s)
I'm going to do some quick calculations here... *typing sounds*... and there you have it! The initial velocity of the jet is the result of that equation. Enjoy your flight!
To find the initial velocity of the jet, we can use the formula:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
In this case, the acceleration (a) is given as 4 m/s^2 and the time (t) is given as 40 seconds.
By substituting the known values into the formula, we can solve for the initial velocity (u):
Final velocity (v) is the takeoff speed.
v = u + at
takeoff speed = u + (4 m/s^2)(40 s)
Since the takeoff speed is achieved at the end of the 40-second period, the final velocity (v) is equal to the takeoff speed. Therefore, we can rewrite the equation as:
takeoff speed = u + (4 m/s^2)(40 s)
Now, we can solve for the initial velocity (u):
u = takeoff speed - (4 m/s^2)(40 s)
Please provide the value for the takeoff speed so that I can calculate the initial velocity.
To find the initial velocity of the jet, we can use the formula:
\(v = u + at\)
Where:
- \(v\) is the final velocity (takeoff speed)
- \(u\) is the initial velocity (what we want to find)
- \(a\) is the acceleration
- \(t\) is the time taken
Given:
- Acceleration (\(a\)) = 4 m/s²
- Time taken (\(t\)) = 40 s
Substituting these values into the formula, we get:
\(v = u + at\)
Rearranging the formula to solve for \(u\):
\(u = v - at\)
Now let's plug in the values:
\(u = \text{takeoff speed} - (4 \, \text{m/s²})(40 \, \text{s})\)
Takeoff speed is not provided in the question, so we'll have to use the given information to find it. Since the jet is accelerating at a constant rate, we can use another formula to find the final velocity:
\(v = u + at\)
Since we want to find the takeoff speed (final velocity), we can use:
\(v = u + at\)
Given:
- Acceleration (\(a\)) = 4 m/s²
- Time taken (\(t\)) = 40 s
- Initial velocity (\(u\)) = ?
Substituting these values into the formula, we get:
\(v = u + at\)
Rearranging the formula to solve for \(v\):
\(v = u + at\)
\(v = u + (4 \, \text{m/s²})(40 \, \text{s})\)
Now we have an equation for both \(u\) and \(v\). By substituting the value of \(v\) from the second equation into the first equation, we can solve for \(u\).