course phy 201
How far does an object travel and what is its acceleration if its velocity increases at a uniform rate from 6 m/s to 30 m/s in 5 seconds?
Explain the meaning of the slope and area of the velocity vs. time for this object during this time interval.
since the acceleration is the change in velocity / the change in elapsed time we need to find these details.
the change in time is the easiest because going for the we start at rest or 0 and we move for 5 secs then we find 5-0= 5 sec for our elapsed change in time.
the change in velocity is just as easy since it gives us the velocity increases so we can determine the change in velocity by 30-6=24m/s.
so acceleration is the change in velocity / the change in elapsed time.
thus change in velocity = 30-6=24m/s
change in time = 5-0=5sec
so 24m/s / 5s = 4.8m/s
24m/s / (5s) = 4.8m/s^2, not 4.8 m/s.
m/s is a unit of velocity, not acceleration.
ok slope is rise over run and the area of the trapezoid is the equalivalent of the acerlation.
the points are graphed and and the right triangle is drawn in. on this graph if you draw in your trapezoids and then find the average points in between each of the given points ou can find your areas from the graph. and you can also find yourself with a contstant acceleration and a linear graph of the velocity vs time which will give you a quadratic equation of a porabola of the position vs time.
I think.
slope is rise / run; since the rise of a v vs. t graph is change in velocity and run is change in clock time, rise / run is change in velocity / change in clock time = average rate of change of velocity with respect to clock time, which is average acceleration.
The average trapezoid 'altitude' for a v vs. t graph approximates the average velocity (since 'altitudes' represent velocities) and trapezoid width represent the duration of the time interval, so area = ave altitude * width represents approximate average velocity * time interval = displacement.
You are reasoning things out according to definitions and conditions, and doing a good job of it. You did make a couple of errors, but on the whole this is very good.
See my notes and be sure you understand; if not, please ask additional questions.