A jet starting from rest reaches a speed of 241km/h on 96.0m of runway. Determine the magnitude of the Jet's acceleration?
Answer is 23.3m/s^2
To determine the magnitude of the jet's acceleration, we can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (241 km/h)
u = initial velocity (0 km/h, as the jet starts from rest)
a = acceleration
s = displacement (96.0 m)
First, let's convert the given velocities from km/h to m/s. We know that 1 km = 1000 m and 1 hour = 3600 seconds, so:
v = 241 km/h * (1000 m/km) / (3600 s/hr) = 67.0 m/s
u = 0 km/h * (1000 m/km) / (3600 s/hr) = 0 m/s
Now, substitute the known values into the equation:
(67.0 m/s)^2 = (0 m/s)^2 + 2 * a * 96.0 m
Simplifying this equation gives:
4489 m^2/s^2 = 2 * 96.0 m * a
Divide both sides of the equation by 2 * 96.0 m to solve for a:
4489 m^2/s^2 / (2 * 96.0 m) = a
This gives:
a ≈ 23.3 m/s^2
Thus, the magnitude of the jet's acceleration is approximately 23.3 m/s^2.
km/h -> m/s,
a=v²/2s