00:02
Starting with acceleration, 12t plus 4, what you need to know is that the derivative of velocity is equal to acceleration.
00:09
So think about a function whose derivative would get you to this.
00:14
And so first thing people think about is t squared because the derivative of t squared is 2t, but then it's actually 6t squared because 6 times 2 would give you that 12 if you follow through the power rule.
00:28
Other people, what they'll do is they'll just look at the exponent, add one to it, and then to 12 divided by that new exponent of 2.
00:36
Same thing with this is 4t, but now we need to add some constant, and it's actually the initial velocity.
00:44
And they tell you in the problem that b of 0 equals 1, so what does that mean for us, is if you plug in 0 for these x's, so that, or sorry, t's 0 plus 0 plus the initial velocity needs equal 1.
00:58
Well, that's why we write it.
01:01
So the actual equation for velocity is 6t squared plus 4t, and the initial velocity is 1, as shown here...