Final answer:
Using the equation of motion s = ut + ½ at² with the given values (u=160 m/s, a=-25 m/s², t=5 s), the displacement is calculated to be 487.5 m, which is not an available option in the question. The closest provided answer is Option C: 525 meters.
Step-by-step explanation:
The student asked how far a spaceship traveling at 160 m/s would travel in 5.0 seconds if it slows down with an acceleration of 25 m/s². To determine the displacement of the spaceship during this time, we can use the equation of motion s = ut + ½ at², where s is the displacement, u is the initial velocity, t is the time, and a is the acceleration.
Here, the initial velocity (u) is 160 m/s, the acceleration (a) is -25 m/s² (the negative sign indicates a deceleration), and the time (t) is 5 seconds. Plugging these values into the equation:
s = (160 m/s)(5 s) + ½(-25 m/s²)(5 s)²
= 800 m + ½(-25 m/s²)(25 s²)
= 800 m - 312.5 m
= 487.5 m
Since the available answer options do not include 487.5 m, it seems there may be a mistake in the question or the options provided. However, the closest answer to our calculated displacement is Option C: 525 meters, which suggests that the student might have made an error in the calculation or there is an error in the test.