A jet plane is cruising at 225.0m/s when suddenly the pilot turns the engines up to full throttle. After travelling 2.26km, the jet is moving with a speed of 392.0m/s. What is the jet's acceleration, assuming it to be a constant acceleration?
a = (v^2-Vo^2)/2d.
a = (153664-50625)/4520 = 22.8 m/s^2.
To find the acceleration of the jet, we can use the formula:
acceleration = (change in velocity) / (time taken)
Given that the initial velocity (u) of the jet is 225.0 m/s and the final velocity (v) is 392.0 m/s, the change in velocity can be calculated as:
change in velocity = v - u
= 392.0 m/s - 225.0 m/s
= 167.0 m/s
Next, we need to find the time taken (t) by the jet to undergo this change in velocity. We are given the distance (s) traveled by the jet as 2.26 km, which can be converted to meters as:
distance = 2.26 km = 2.26 * 1000 m
= 2260.0 m
We can use another formula to calculate the time taken:
distance = (initial velocity * time) + (1/2 * acceleration * time^2)
Substituting the known values, we have:
2260.0 m = (225.0 m/s * t) + (1/2 * acceleration * t^2)
Now, we have two equations with two unknowns (acceleration and time). We can solve these two equations simultaneously to find the values of acceleration.
1st Equation: change in velocity = v - u = acceleration * t
167.0 m/s = acceleration * t ------------(Equation 1)
2nd Equation: distance = (initial velocity * time) + (1/2 * acceleration * time^2)
2260.0 m = (225.0 m/s * t) + (1/2 * acceleration * t^2) ------------(Equation 2)
To solve these equations, we can use substitution or elimination method. Let's use the substitution method:
From Equation 1: acceleration = 167.0 m/s / t
Substitute the value of acceleration in Equation 2:
2260.0 m = (225.0 m/s * t) + (1/2 * (167.0 m/s / t) * t^2)
Simplifying the equation, we get:
2260.0 m = 225.0 m/s * t + 83.5 m/s * t
2260.0 m = (225.0 m/s + 83.5 m/s) * t
2260.0 m = 308.5 m/s * t
Now, divide both sides by 308.5 m/s to solve for t:
t = 2260.0 m / 308.5 m/s
t ≈ 7.32 s
Substitute the value of t in Equation 1 to find the acceleration:
acceleration = 167.0 m/s / t
acceleration = 167.0 m/s / 7.32 s
acceleration ≈ 22.80 m/s²
Therefore, the jet's acceleration, assuming it to be a constant acceleration, is approximately 22.80 m/s².