00:01
We're given the acceleration which i see is constant and we're also given the velocity at time zero.
00:11
Let's find an expression for v as a function of time.
00:18
The x component of acceleration is equal to the derivative of the x component of velocity with respect to time and the y component of acceleration is equal to the derivative of the y component of velocity with respect to time.
00:36
So if we integrate both sides we see that the x component of velocity as a function of time is equal to the integral of ax dt.
00:48
Similarly for y.
00:57
So let's plug these in.
00:58
We have the integral of positive four.
01:07
So this is four dt which is just equal to four t plus the constant c.
01:18
We'll call that c1.
01:20
Then we have negative five for the y component.
01:26
So we get negative five t plus another constant.
01:30
I'll call c2.
01:32
We can solve for the constants using this initial condition here.
01:39
So we have that v of x at time zero is equal to negative two.
01:49
So negative two equals four times zero plus c1 which is just c1.
01:57
So c1 is negative two.
01:59
Then we have vy at zero is equal to positive two.
02:04
So we have two equals negative five times zero plus c2 which is just c2.
02:12
So we have, i'll just fill that in over here, v of t is equal to four t plus c1 which is minus two.
02:30
I hat plus negative five t plus c2 which is two.
02:40
J hat.
02:42
The units are meters per second.
02:48
I'm going to make some space here.
02:52
So in part a we want to find the velocity at t equals two seconds.
02:58
So this is four times two minus two.
03:02
I hat plus negative five times two plus two.
03:10
J hat and meters per second.
03:16
Okay so this is equal to eight minus two which is six.
03:21
So six i hat and then we have negative 10 plus two which is negative eight.
03:27
J hat meters per second.
03:32
So this is the velocity at t equals two seconds.
03:40
Next we're given that at time t equals zero the particle passes through the origin...