00:01
Hello, here we have to solve the following problem.
00:03
Based on the graph for speed as velocity as a function of time, we first have to sketch x as a function of time and acceleration as a function of time.
00:18
Let's do that.
00:19
But first of all, we will look at the graph for the velocity.
00:24
And from here, we can see that from 0 to 4 seconds.
00:31
Acceleration is constant and this acceleration is 2 meters per second minus negative 2 meters per second or 4 seconds which is 1 meters per square second therefore in this time interval x as a function of time is negative 2 t plus t squared over 2 let's see when this function becomes 0 so that is 0 when t over 2 times t plus sorry t minus 4 is 0 therefore it becomes 0 when time is 0 seconds and when time is 4 seconds let me see if i'm missing any other solution.
02:00
Now these are zeros of the function.
02:02
And now let's calculate the derivative to determine it as a minimum or maximum.
02:08
So the derivative of this function is t minus 2.
02:14
Therefore, if we plot the derivative, so it is negative before 2 and positive after 2, therefore the main function x decays before 2 and grows after 2, then 2 is a point of minimum.
02:43
Let's calculate x at 2.
02:46
At 2, x is negative 4 plus 4 over 2 meters, which is negative 2 meters.
02:57
So, and after, in the interval from 4 to 10 seconds, x equals to the following.
03:16
So, the that is x at 0 at 4 plus speed of 2 meters per second times t minus 4 that is x at 0 as we already shown is 0 therefore this x equals to 2 times t minus 4 now we can sketch yeah let's start sketching this coordinate x as a function of time.
04:04
Here i will do a quality of sketch...