Final answer:
Jeremy's average rate of acceleration while merging with traffic is -1.8 m/s², indicating he is accelerating in the southward direction, opposite of the positive (northward) direction. Option B is correct.
Step-by-step explanation:
Jeremy's average rate of acceleration can be calculated using the formula for acceleration, which is the change in velocity divided by the time taken for that change. In this case, since we're assuming north as the positive direction and Jeremy is traveling south, his initial velocity is -9 m/s, and his final velocity when he merges is -20 m/s. The time taken for this change is 6 seconds.
To find the acceleration, we subtract the final velocity from the initial velocity, then divide by the time interval:
a = (vf - vi) / t
So we have:
a = (-20 m/s - (-9 m/s)) / 6 s
a = (-20 + 9) / 6 m/s²
a = -11 / 6 m/s²
a = -1.8 m/s²
Therefore, Jeremy's average acceleration is -1.8 m/s², which indicates it is in the opposite direction of the defined positive (south), hence the negative sign.
To find Jeremy's average rate of acceleration, we can use the formula:
Acceleration = (Final Velocity - Initial Velocity) / Time
Jeremy's initial velocity is 9 m/s south and his final velocity is 20 m/s. The time taken is 6 seconds. Plugging these values into the formula, we get:
Acceleration = (20 m/s - 9 m/s) / 6 s = 11 m/s / 6 s = -1.8 m/s²
Therefore, Jeremy's average rate of acceleration during this period is -1.8 m/s².