Randall D. Knight — Kinematics in One Dimension: Problem Challenge_Problem_85

The Starship Enterprise returns from warp drive to ordinary space with a forward speed of \(50\text{ km/s}\). To the crew’s great surprise, a Klingon ship is \(100\text{ km}\) directly ahead, traveling in the same direction at a mere \(20\text{ km/s}\). Without evasive action, the Enterprise will overtake and collide with the Klingons in just slightly over \(3.0\text{ s}\). 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 \(x_0 = 0\text{ km}\) 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.