motion graph?

Question

A ball is thrown vertically upwards with a speed of 20m/s. Draw a graph showing the velocity of the ball as a function of time as it goes up and then comes back.

Answer 1

An equation which relates the velocity (v) of the ball as a function of time (t) would be,
v = v_0 + a * t
where v_0 is the ball's initial velocity, and a is some acceleration the ball experiences.

In this case, the ball's initial velocity (v_0) is 20 m/s in the upwards direction, which will we also define as the positive direction.
The ball's acceleration is in the downward, negative, direction due to the force of gravity exerted on the ball with a magnitude of 9.81 m/s.

Knowing this information, we can re-write our above equation as,
v = 20 m/s - 9.81 m/s^2 * t
So now we have a function of velocity with respect to time which we can graph.

Does this equation look familiar? Can you tell anything about the slope or shape of this graph?
What if we re-wrote it like this,
y = 20 - 9.81x

The graph is linear. The graph has a Y-intercept at Y=20, X=0, and slopes down at a constant rate of 9.81. The graph intersects the X axis at Y=0, X=2.04.

Mathematically, you can extent the graph upward for negative values of x (or t), byt physically this does not make sense since that would mean the time before the ball was thrown.
But it does make both mathematical and physical sense to extend the graph down below the X intercept since just because the ball's velocity is zero does not mean that is finished yet...it now has to fall back down to the ground.

It takes just as much time for the ball to fall back down to the Earth as it does to climb up to its highest altitude. We should continue the graph on for another 2.04 seconds (total of 4.08 seconds) until the ball reaches the ground.
Notice that at no time during this process did the slope of the line change...it was always at a constant -9.81 and the graph is just a straight line.


EDIT:
The velocity of the ball is always decreasing from some maximum positive value.
Speed on the other hand is the magnitude of velocity. If the velocity is 5 m/s (in some direction), the speed if 5 m/s. If the velocity is -5 m/s (in some direction), the speed is still 5 m/s, not -5 m/s. So if you were to graph speed instead of velocity, you would get a V shaped graph with the point of the V at the X intercept I calculated earlier. Graphing speed v. time would be the same as graphing the absolute value of velocity v. time, s = abs( v(t) ).
But then, you asked to graph velocity.

Answer 2

do you already know calculus? properly..the 1st part of the question I have not any clue what that's, i've got on no account seen a action graph or an acceleration graph that used arrows. yet for an acceleration vs timegraph, thats trouble-free. The by-made of a speed time graph is an acceleration time graph, and the 2d by-made of a displacement time graph is an acceleration graph. by-product is the cost of exchange, or the slope at each and each element.

Answer 3

It would look like a "V" - with the sides bowed inward toward each other. Max velocity at time = 0, velocity slowing gradually slowing down to 0 at maximum altitude, and then velocity gradually increasing as it falls back to earth.