Question

The Starship Enterprise returns from warp drive to ordinary

space with a forward speed of 50 km/s. To the crew’s great surprise,

a Klingon ship is 100 km directly ahead, traveling in the

same direction at a mere 20 km/s. Without evasive action, the

Enterprise will overtake and collide with the Klingons in just

slightly over 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.

Hint: Draw a position-versus-time graph showing the motions

of both the Enterprise and the Klingon ship. Let x0 = 0 km be

the location of the Enterprise as it returns from warp drive. How

do you show graphically the situation in which the collision is

“barely avoided”? Once you decide what it looks like graphically,

express that situation mathematically.

Short answer

The kinematic equations of motion at constant acceleration is given by :

Step-by-step solution

The graph plot:

Calculation of the acceleration:

The position function for the starship at 3 seconds is given by :