Final answer:
To find the time for a spaceship to accelerate from 11.1 km/s to 11.7 km/s over a distance of 1220 km, we convert units and use kinematic equations to calculate acceleration and time.
Step-by-step explanation:
The student's question refers to determining the time required for a spaceship to increase its speed from 11.1 km/s to 11.7 km/s given that the spaceship travels 1220 km with uniform acceleration. To solve this question, we can use the kinematic equation that relates displacement (s), initial velocity (v0), final velocity (v), acceleration (a), and time (t):
s = v0t + 0.5at2
Firstly, we need to convert the velocities to m/s by multiplying the given values by 1000:
- Initial velocity, v0 = 11.1 km/s × 1000 = 11100 m/s
- Final velocity, v = 11.7 km/s × 1000 = 11700 m/s
Next, convert the displacement to meters:
- Displacement, s = 1220 km × 1000 = 1220000 m
Now we rearrange the equation to solve for time (t):
t = ∀/a
Since we have displacement and the velocities, we can calculate acceleration (a) using the formula:
v2 = v02 + 2as
Which rearranges to:
a = (v2 - v02)/2s
Substituting our known values:
a = (117002 - 111002)/ (2 × 1220000) m/s2
After calculating the acceleration, we can then calculate the time using our rearranged kinematic equation. In this context, the correct answer will be one of the provided options (A, B, C, or D).