00:01
In this question we are given a position versus time function for a ball and we are asked to perform a number of calculations with it, including generating some values and plotting those values.
00:15
So to find the initial position, initial velocity, and acceleration of the ball, we're first going to notice that this equation follows our basic position versus time function for uniformly accelerated motion, which is x equals x -naught plus v -naught t plus one -half a t squared.
00:34
And from this, we can see that x -naught must be zero meters because there is no constant term over here, in other words, a term without t.
00:48
And then v -naught is going to be the coefficient of the linear term, so 5 .0 meters per second.
01:00
And then one -half of a is equal to the coefficient of the quadratic term, so that tells us then that our acceleration is going to be negative 20 meters per second squared.
01:16
And next we're asked to plot x versus t for zero to two seconds.
01:23
So first of all, let's generate those values really quickly and then i will add a plot that i've made elsewhere.
01:30
So we'll have t and then we're going to have 5t minus 10t squared.
01:39
And then we'll finally have a column for that actual position value.
01:43
So when t is zero, 5 times zero minus 10 times zero squared is zero.
01:53
When t is one, we're going to have 5 times one minus 10 times one squared, which gives negative five.
02:02
And then when t is two, we will have 5 times two minus 10 times two squared, which gives me negative 30.
02:15
And give me just a moment.
02:18
I'm going to pause the video and then add a screenshot of the graph.
02:24
I did not connect the lines on this plot and i realize the values are a little bit hard to read.
02:36
But here is...
02:37
Whoa! let's go back to draw...