Final answer:
Using the kinematic equation, we solve for the distance traveled by an object accelerating uniformly from rest. After finding the acceleration to be 27.8226 m/s², we calculated the distance to be approximately 2138.4 meters in 12.4 seconds.
Step-by-step explanation:
To calculate how far an object travels while accelerating from rest, we can use the kinematic equation for uniformly accelerated motion:
S = ut + ½at²
where:
- S is the displacement (distance traveled)
- u is the initial velocity (which is 0 m/s because the object starts at rest)
- t is the time (12.4 seconds)
- a is the acceleration
To find the acceleration, we use the formula:
a = (final velocity - initial velocity) / time
a = (345 m/s - 0 m/s) / 12.4 s = 27.8226 m/s²
Now plug the acceleration and time into the displacement equation:
S = (0 m/s × 12.4 s) + ½(27.8226 m/s² × (12.4 s)²)
Simplify and calculate the displacement:
S = 0 + ½(27.8226 m/s² × 153.76 s²)
S = ½(4276.798976 m)
S = 2138.399488 m
Therefore, the object travels approximately 2138.4 meters in 12.4 seconds, denoting none of the options is correct.