00:01
Hi there, so for this problem, the information that we are given is that the velocity function b is equal to 44 this plus 2 .2 times the time.
00:19
And where the time is measuring seconds.
00:24
And so the question is how far just the core trouble between the time that the driver hits the gas pedal that will correspond to the time equals to zero? and the time that the car reaches the speed of 60 miles per hour.
00:36
This is at the speed that corresponds in feet per second to 88 feet per second.
00:51
So with that said, we are asked to answer how far does the car travel? so we need to obtain some distance.
01:03
So the first thing that we need to know is that the speed is the rate of change of the position with respect the time.
01:12
So if we want the distance in this case, that will be the integral, and this from zero to some time, this, well, let's call that the time one, that is the time at which we obtain that speed of the speed function integrated over the time.
01:35
So first of all, we need to obtain the time one.
01:38
So the time one is when we obtain 88 in this speed.
01:43
So we just set that to the expression that we are given, and then solve for the time one.
01:50
So you can see that this will be 44 divided by 2 .2...