course PHY201
An automobile traveling a straight line is at point A at clock time t = 4 sec, where it is traveling at 10 m/s, to point B at clock time t = 11 sec, where it is traveling at 20.5 m/s. Point A is 75 meters from the starting point and point B is 115 meters from the starting point. What are the average velocity and the average acceleration of the automobile during the specified time? What evidence is there that the acceleration is or is not uniform?
vAve = ds/dt = (115m - 0m) / (11s - 0s) = 10.45 m/s
This assumes that the position was 0 when t = 0. That is not necessarily the case. The clock does not necessarily start at any pre-assumed position or velocity.
The only information you have is on the interval. Most of the rest of your comments are confined to what happens on the interval, and your observations are very good.
There is a lot to consider here in this equation. There is definently no uniform acceleration here. Reason for my thoughts as to so, is look at the distance covered: 115m. With the first distance 75m.
115m - 75m = 40m
Now look at the velocities. how can you more than double the velocity in such a short distance of 40m, yet the time interval is 7s? this also assumes information that wasn't given (i.e., assumes position 0 at t = 0).
Also between point A and point B, you cover 75m in 4s with a velocity of 10m/s?
75m / 4s = 18.75m/s
The only thing I can think of is a vehicle took off from the starting point under full load/maxium acceleration on a race course similiar to an auto-cross event environment of many curves that would explain for rapid acceleration and decceleration changes and different time intervals between points of different distances."
You are right about ample evidence that acceleration is not uniform, and you specify at least a couple valid contradictions of this assumption.
You can nevertheless calculate the average velocity and the average acceleration over the interval.. You have already noted that the object travels 40 cm in 4 seconds. You also know the velocities at the beginning and end of this interval.
Generally:
&#Average velocity is defined as average rate of change of position, vAve = `ds / `dt.Average velocity is equal to the average of initial and final velocities, (vf + v0) / 2, if acceleration is uniform. If average velocity is not equal to the average of initial and final velocities, then acceleration is not uniform. This information can be used to determine whether or not acceleration is uniform. What is your conclusion? &#