00:01
So in this problem, when we have a car, it's traveling at 24 .6 meters per second.
00:09
It's hitting the brakes so that it is accelerating at 4 .92 meters per second, slowing meters per second squared, slowing down.
00:23
So in part a, we want to find the time it takes to stop.
00:29
And so we use one of the kinematic equations.
00:32
Velocity is equal to initial velocity plus exclamation times time.
00:39
So what we'll do here first is put a quick axis on, starting zero and going in the x direction.
00:50
We'll use that more for the later parts.
00:52
But we have everything here so we can start.
00:56
We can solve this first for time and begin plugging in.
01:04
The final velocity is zero because it's completely stopped minus the initial velocity that we were given over the given acceleration.
01:20
It is negative here because the acceleration is in the opposite direction of the motion and by this axis also.
01:30
And that's important because that means that we would get a positive five seconds in time, which has to be the case because time should always be positive.
01:42
So in part b, we want to find the distance and stop set.
01:46
We'll use another kinematic equation.
01:50
The distance is equal to the initial distance plus initial speed times time, plus one -half acceleration time squared.
02:02
We picked our axis to start at zero, which is really convenient to do.
02:08
So this term falls out, and we can plug in the initial velocity as given, the time that we found in part a, and the acceleration, again, making sure that it is negative and the time again, which just worked out to 61 .5 meters.
02:44
So in part c, we want to graph these relations, first in the distance over time, and then in the velocity over time.
03:10
And so if we look at the end, the equation for velocity we have a negative time squared term which means we'll end up having some parabola and it'll be upside down and we know how long it takes it takes five seconds and we know the distance 61 .5 and so the graph looks something like this you can plot that in your calculator or in excel more precisely but that's what it should look something like and then if we go look back in part a and our equation for velocity, we see that we have a negative time term because acceleration is negative, which means we have a linear relationship and it will be angled.
04:09
And so the velocity starts high, goes linearly down in five seconds from the initial 24 .6...