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A ball is tossed upward with an initial velocity of 25 meters / second. Assume that the acceleration of gravity is 10 m/s^2 downward.
· What will be the velocity of the ball after one second?
answer/question/discussion: 25m/s – 10m/s/s after 1 sec = 15m/s ???
· What will be its velocity at the end of two seconds?
answer/question/discussion: 25m/s – 10m/s/s – 10m/s/s (after 2 seconds) = 5m/s/ ???
· During the first two seconds, what therefore is its average velocity?
answer/question/discussion: 25m/s + 5m/s / 2 = 15m/s
· How far does it therefore rise in the first two seconds?
answer/question/discussion: ‘dv / ‘dt = 20m/s / 2sec = 10m
20m/s / 2sec = 10 (m/s) / s = 10 m/s * 1/s = 10 m/s^2, not 10 m.
This would be the acceleration of an object whose velocity changes by 20 m/s in 2 s. If the upward direction is positive, this object has a velocity change of -20 m/s so its acceleration is -10 m/s.
However the question asked for displacement. You can't get displacement from change in velocity and change in clock time.
You can get displacement from average velocity and change in clock time.
What therefore is the displacement of this object?
· What will be its velocity at the end of a additional second, and at the end of one more additional second?
answer/question/discussion: after 3 seconds = -5m/s, after 4 seconds = -15m/s
· At what instant does the ball reach its maximum height, and how high has it risen by that instant?
answer/question/discussion: the ball reaches its maximum height at v = 0. v^2 – vo^2 / 2a = (25m/s)^2 / 2(-10m/s) = 31.25m
· What is its average velocity for the first four seconds, and how high is it at the end of the fourth second? (25+-5) / 2 =10m/s
answer/question/discussion: (25+-5) / 2 =10m/s
displacement = average velocity * change in clock time
You have just found the average velocities for these intervals.
What is the change in clock time for each of the intervals?
What therefore is the displacement for each of the intervals?
· How high will it be at the end of the sixth second?
answer/question/discussion: ???
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1 hour, maybe a little less.
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I spent way too much time on this. I just don't get it. I tried to use the book and it helped a little with the height of the ball at v=0 but i'm kinda lost.
You got everything except the answers related to displacement. In each of those situations you know average velocity and time interval, so you can use the definition of average velocity to find the displacement.
You also know initial velocity, final velocity and change in clock time for each of those intervals, so you could use the equatios of uniformly accelerated motion. However it's better that you reason out the answers conceptually, using the definitions.
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