An aircraft decelerates at 0.5m/s. After 8 minutes it dropped to 160m/s. Find its initial velocity.
v =Vi + a t
v= 160
t = 8*60 = 480 s
a = -0.5 m/s^2 (I assume you mean)
160 = Vi - 0.5 *480
Vi = 160 + 240 = 400 m/s
Well, it seems like this aircraft is really taking its time to slow down. Maybe it's having a mid-air spa treatment or something. Anyway, let's solve this puzzle.
We know that the deceleration of the aircraft is 0.5 m/s, and we can convert 8 minutes to seconds by multiplying it by 60 (since there are 60 seconds in a minute). So, 8 minutes is equal to 480 seconds.
Using the formula of linear motion v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration (deceleration in this case), and t is the time, we have:
160 = u + 0.5 * 480
Now, all we have to do is solve this equation for u, the initial velocity. Let me grab my calculator...
*Beep boop beep*
After crunching the numbers, it looks like the initial velocity of this aircraft is 400 m/s. So, it went from really speedy to not-so-speedy in 8 minutes. Time for these planes to hit the gym, I guess!
To find the initial velocity of the aircraft, we need to use the formula for deceleration:
Final velocity (V) = Initial velocity (U) - (Deceleration (a) * Time (t))
Given:
Final velocity (V) = 160 m/s
Deceleration (a) = -0.5 m/s (Note: the negative sign indicates deceleration)
Time (t) = 8 minutes = 8 * 60 = 480 seconds
Substituting the given values into the formula:
160 = U - (-0.5 * 480)
Simplifying the equation:
160 = U + 240
Subtracting 240 from both sides:
160 - 240 = U
-80 = U
Therefore, the initial velocity of the aircraft was -80 m/s. Note that the negative sign indicates that the aircraft was moving in the opposite direction of the deceleration.
To find the initial velocity of the aircraft, we can use the formula for uniformly decelerating motion:
v = u + at
Where:
- v is the final velocity (160 m/s in this case),
- u is the initial velocity (what we want to find),
- a is the deceleration rate (-0.5 m/s² in this case), and
- t is the time taken (8 minutes = 480 seconds in this case).
First, convert the time from minutes to seconds by multiplying it by 60:
t = 8 minutes * 60 seconds/minute = 480 seconds
Now we can substitute the given values into the formula and solve for u:
160 m/s = u + (-0.5 m/s²) * 480 seconds
To isolate u, we can simplify and rearrange the equation:
160 m/s = u - 0.5 m/s² * 480 seconds
160 m/s + 0.5 m/s² * 480 seconds = u
Now let's calculate the result:
160 m/s + 0.5 m/s² * 480 seconds = u
160 m/s + 240 m/s = u
400 m/s = u
Therefore, the initial velocity of the aircraft was 400 m/s.