A spaceship is approaching Starbase Beta at an initial velocity of 130 km/s in t

Question

A spaceship is approaching Starbase Beta at an initial velocity of 130 km/s in the +x direction. The ensign sets its computer to initiate a braking program starting at time t = 0. After this time, the computer controls the ship until the ship docks at time t = T so that its x-acceleration is ax (t) = b(t ? T), where b = 0.29 m/s3. Note that ax < 0 for t < T, but gets smaller as t approaches the docking time T. (a) What must T be so that the ships x-velocity is also zero at the time of docking? (b) How far is the ship from the station at t = 0?

Explanation / Answer

dv = a dt...integrating from 0 to T...and putting final velocity = 0...we get...T = 946.86 s...(for b = 0.29)...but somewhere i saw a similar question with b= .26....in that case, T = 1000 s..... d^s/dt^2 = a....solving this...for a = b(t-T)...we get...s = bT^3 / 6..... Putting b = 0.29...and T = 946.86 s....we get...s = 41040.24 KM.... Putting b = 0.26...and T = 1000s...we get....43333.33 KM...

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