The Starship Enterprise returns from warp drive to ordinary space with a forward

Question

The Starship Enterprise returns from warp drive to ordinary space with a forward speed of 55 km/s . To the crew's great surprise, a Klingon ship is 100 km directly ahead, traveling in the same direction at a mere 22 km/s . Without evasive action, the Enterprise will overtake and collide with the Klingons in just about 3.0 s . The Enterprise's computers react instantly to brake the ship.The Starship Enterprise returns from warp drive to ordinary space with a forward speed of 55 km/s . To the crew's great surprise, a Klingon ship is 100 km directly ahead, traveling in the same direction at a mere 22 km/s . Without evasive action, the Enterprise will overtake and collide with the Klingons in just about 3.0 s . The Enterprise's computers 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.

Explanation / Answer

this can be seen as a single object with the speed of (55 - 22) km/s that is the relative speed between enterprise and klingon ship

distance by which it need to stop = 100 km

by third equation of motion

v^2 = u^2 + 2as

final velocity will be 0

0 = (55 - 22)^2 + 2 * a * 100

a = -5.445 km/s^2

acceleration that enterprise needs = -5.445 km/s^2

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