#$&*
course PHY 241
445pm 10/22/2011
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?
Assuming that the starting point is at 0 meters and clock time t = 0 s and the vehicle starts from rest.
t_start = 0 s
t_A = 4 s
t_B = 11 s
v_start = 0 m/s
v_A = 10 m/s
v_B = 20.5 m/s
x_start = 0 m
x_A = 75 m
x_B = 115 m
average velocity from starting point to point B
v_ave = 'dx/'dt
= (115m / 11s)
= 10.5 m/s
average velocity from starting point to point A
v_ave = 'dx/'dt
= (75 m / 4 s)
= 18.8 m/s
@& You are assuming the state of motion at t = 0. No information was given about that instant, and there is no guarantee that the car was even in motion at t = 0. t = 0 could well just be when someone happened to start the clock.
So neither of these intervals is relevant, though if your assumption is correct your work would be correct.*@
average velocity from point A to point B
v_ave = 'dx/'dt
= (115m - 75m)/(11s-4s)
= 14.5 m/s
average acceleration from starting point to point B
a_ave = 'dv/'dt
= (20.5 m/s / 11 s)
= 1.86 m/s^2
average acceleration from starting point to point A
a_ave = 'dv/'dt
= (10 m/s / 4 s)
= 2.5 m/s^2
average acceleration from point A to point B
a_ave = 'dv/'dt
= (20.5 m/s - 10 m/s) / (11 s - 4 s)
= (10.5 m/s / 7 s)
= 1.5 m/s^2
I was unclear what you meant by 'specified time', so I answer specified time from a number of different intervals.
The acceleration is NOT uniform based on the answers or average acceleration from starting point to point A, which is 2.5 m/s^2 and average acceleration from Point A to Point B, which is 1.5 m/s^2
"
@& The only information you have is for the interval from A to B.
The wording could have been clearer; 'specified time' should have read 'specified time interval', which would likely have clarified this.
You can draw a conclusion about uniformity of acceleration just on the interval from A to B. If the average velocity, which you have calculated correctly, is not equal to the average of initial and final velocities then the v vs. t graph isn't a staight line, and acceleration cannot be uniform.*@