The Starship Enterprise returns from warp drive to ordinary space with a forward speed of 53km/s.To the crew's great surprise,a Klingon ship is 140km directly ahead,traveling in the same direction at a mere 20km/s.Without evasive action,the Enterprise will overtake and collide with the Klingons in just about 4.2s.The Enterprise's puters react instantly to brake the ship.What magnitude acceleration does the Enterprise need to just barely avoid a collision with the Klingon ship?Assume the acceleration is constant. 英语
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【答案】 Enterprise's speed is V1=53km/s
Klingon's speed is V2=20km/s
let's suppose Enterprise's acceleration ：a=?km/s^2
suppose accelere time：t=?s
an Uniformly retarded rectilinear motion
→with Enterprise S1=V0t+1/2at^2=53*t+1/2at^2 ①
→with Klingon S2=Vt=20*t②
to barely avoid a collision
→S1=S2+140KM③
solve①,②and③
a≈-3.8893km/s^2
Anather way
if Enterprise can reduce the speed to 20km/s in the 140km,it can barely avoid a collision!
so this question became → S=1/2at^2
use average speed → V=[0+（53-20）]/2=16.5km/s
so S=V(average speed)*t → t=140/16.5
so acceleration a=△V/t=(-33)/(140/16.5)=-3.8893