A jet aircraft has a mass of 4,500 kg and has an engine that exerts 60,000 newtons.
a. What is the jets acceleration.
b. What is the speed of the jet when it reaches 8 seconds
c. what is the distance traveled at 8 seconds
a. What is the jets acceleration.
b. What is the speed of the jet when it reaches 8 seconds
c. what is the distance traveled at 8 seconds
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Well, with the information the question gave us, we can use Newton's 2nd law of motion F= M x a (where F is the force exerted, M is the mass the force is exerted on and a is the acceleration) to find out the acceleration in part a. correct me if I'm mistaken but my calculations result in a = 13.33 ms^-2.
now using the given acceleration and time t = 8 we can use the UARM(uniformly accelerated rectilinear motion laws)
UARM formulas: ( V = velocity, Vo = initial velocity, a = acceleration, x = displacement/position, t = time )
1.V = Vo + at
2.V^2 = Vo^2 + 2ax
3.x = Vo*t + 1/2(a*t^2)
picking #1 we substitute a=13.33 and t=3 Vo=0 (assuming the aircraft was initially at rest) so,
V =0 + 13.33(8) = 106.64 m/s
now to find the distance traveled x we can use equation number 2 or 3, for the sake of our laziness, let's use #2 and a trusty cellphone calculator:
so, 106.64^2 = 0^2 + 2(13.33)(x), x = 426.56 m
Again, I'm not sure of my arithmetic but I hope this helps!
now using the given acceleration and time t = 8 we can use the UARM(uniformly accelerated rectilinear motion laws)
UARM formulas: ( V = velocity, Vo = initial velocity, a = acceleration, x = displacement/position, t = time )
1.V = Vo + at
2.V^2 = Vo^2 + 2ax
3.x = Vo*t + 1/2(a*t^2)
picking #1 we substitute a=13.33 and t=3 Vo=0 (assuming the aircraft was initially at rest) so,
V =0 + 13.33(8) = 106.64 m/s
now to find the distance traveled x we can use equation number 2 or 3, for the sake of our laziness, let's use #2 and a trusty cellphone calculator:
so, 106.64^2 = 0^2 + 2(13.33)(x), x = 426.56 m
Again, I'm not sure of my arithmetic but I hope this helps!
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Acceleration = Force ÷ Mass = 60,000 ÷ 4500 = 13.333 m/s^2
vf = vi + a * t, vi = 0
vf = 13.333 * 8 = 106.667 m/s
d = vi * t + ½ * a * t^2
d = ½ * 13.333 * 64 = 426.656 m
For a more exact answer, d = ½ * 13⅓ * 64 = 426.667 m
Check:
Distance = Average velocity * time
Distance = ½ * (vi + vf) * t = ½ * 106⅔* 8 = 426.667 m
vf = vi + a * t, vi = 0
vf = 13.333 * 8 = 106.667 m/s
d = vi * t + ½ * a * t^2
d = ½ * 13.333 * 64 = 426.656 m
For a more exact answer, d = ½ * 13⅓ * 64 = 426.667 m
Check:
Distance = Average velocity * time
Distance = ½ * (vi + vf) * t = ½ * 106⅔* 8 = 426.667 m