00:01
So in this problem, we have blake running in a race.
00:04
Part of this race is a track with a circle of 60 meters diameter, and we want to find the centripetal acceleration.
00:12
So we know blake runs 400 meters in 47 .3 seconds.
00:21
So to find centripetal acceleration, the formula for such is the centripetal acceleration, also known as the radial acceleration, a rad, is equal to v squared.
00:32
Over r.
00:34
V being the tangential speed of the object in motion around the center.
00:42
So we want to find v, and we can do that from the given information, where velocity is defined as a change in position, over change in time, and then we have the position as 400 meters and the time 47 .3 seconds.
01:02
So the velocity is equal to 8 .46.
01:09
Meters per second.
01:14
We'll then plug that in to the acceleration formula and then the radius as given to find centripetal acceleration in this first case, part a, as 1 .19 meters per second squared.
01:39
So in part b, we have the same circular track, but now the acceleration is given as 2 .18 meters per second squared, and we want to find the time to complete the whole lap.
02:01
Well, so once again, velocity is the change in position over the change in time, and we need to plug us in algebraically now.
02:13
So when we square it, we get delta x squared over t squared.
02:24
And plugging in now, we end up with delta x squared over t squared times r.
02:37
So we are given a and we're given x.
02:41
It's the same 400 meters...