Calculating Acceleration?
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How would you calculate the acceleration of a space shuttle in m/s^2 when this is the information given: In the 74 seconds after lift-off, the space shuttle Challenger travels 36km. Assuming constant acceleration, calculate the acceleration of the shuttle in m/s^2. Please help! The answers say it is 13m/s^2 [forward] I can never get that answer :S
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Answer:
You need to use the formula x=x0+v0t+(1/2)*a*t^2 x=final position , x0=initial position , v0=initial velocity , t=time , a= acceleration You know that the final position is 36km which is 36000m, the initial position is zero, the initial velocity is zero, and the time is 74 seconds. So after cancelling out the zero parts you are left with the formula x=(1/2)*a*t^2 ---> a=2x / t^2 a=2(36000m) / (74s)^2 a=13.15 m/s^2
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Other answers
I'd use the "no final velocity" constant acceleration kinematics equation x_f = x_i + (v_i) t + ½a t² If we choose the origin to be at the launch point, and positive upward, then x_f = 36 km = 36000 m x_i = 0 m v_i = 0 m/s t = 74 s Substitute the zero values and solve for "a". x_f = 0 + 0 + ½a t² a = 2x_f / t² = 2(36000 m) / (74 s)² = 13 m/s² (Um ... by "no final velocity" I meant that the equation doesn't involve the final velocity, not that the space shuttle has "no final velocity".)
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