Final answer:
The time required for a spaceship to accelerate from 14.8 km/s to 17.6 km/s while covering 1257 km can be calculated using kinematic equations. The problem requires initially calculating the acceleration and then finding the time using that acceleration and the given distances.
Step-by-step explanation:
To calculate the time required for the spaceship to increase its speed from 14.8 km/s to 17.6 km/s while covering a distance of 1257 km with constant uniform acceleration, we need to use the kinematic equations of motion. We are provided with the initial velocity (vi), final velocity (vf), and the distance (d) covered. The relevant kinematic equation linking these variables with time (t) and acceleration (a) is:
vf = vi + a × t
We first need to calculate the acceleration using the formula:
a = (vf - vi) / t
Then, we use another kinematic equation to find the time:
d = vi × t + (1/2) × a × t2
Because we don't have the time directly, we'll need to solve these equations simultaneously. First, we solve for acceleration, then substitute back into the second equation to find the time.