WEBVTT
00:00:01.600 --> 00:00:10.600
An object has an initial velocity that increases to 14 meters per second as the object accelerates in the direction of its velocity.
00:00:11.600 --> 00:00:21.040
The object accelerates along a 17.1-meter-long straight line at a rate of five meters per second squared.
00:00:21.920 --> 00:00:24.280
What is the object’s initial velocity?
00:00:25.600 --> 00:00:30.320
Alright, so in this question, we’re trying to find out the object’s initial velocity.
00:00:31.360 --> 00:00:36.000
We’re told that the object starts with this initial velocity.
00:00:36.720 --> 00:00:41.680
And then, its velocity increases to 14 meters per second.
00:00:42.440 --> 00:00:46.840
The way it does this is by accelerating in the direction of its velocity.
00:00:47.560 --> 00:00:51.920
And this acceleration is five meters per second squared.
00:00:52.760 --> 00:01:00.160
We’re also told that the object is moving along a 17.1-meter-long straight line.
00:01:01.040 --> 00:01:03.880
So let’s label all of this information with symbols.
00:01:04.920 --> 00:01:08.920
Firstly, we’re trying to find out the object’s initial velocity.
00:01:09.600 --> 00:01:11.520
Let’s call this 𝑢.
00:01:12.400 --> 00:01:15.720
And we don’t know what that is, so a question mark.
00:01:16.600 --> 00:01:20.040
Secondly, we know the final velocity of the object.
00:01:20.560 --> 00:01:22.000
Let’s call this 𝑣.
00:01:22.520 --> 00:01:25.400
And we know that that’s 14 meters per second.
00:01:26.360 --> 00:01:28.840
Thirdly, we also know the acceleration of the object.
00:01:29.200 --> 00:01:31.120
We’re gonna call this 𝑎.
00:01:31.600 --> 00:01:35.880
And we know that 𝑎 is equal to — now, we’re told that the object accelerates in the direction of its velocity.
00:01:36.560 --> 00:01:42.840
So if the object is moving towards the right, then it also accelerates towards the right.
00:01:43.880 --> 00:01:48.760
Of course, it doesn’t say anywhere that it’s moving towards the right.
00:01:49.320 --> 00:01:52.680
But we can choose which direction the object is moving.
00:01:53.400 --> 00:01:56.880
The point is that the acceleration is in the same direction as its velocity.
00:01:57.440 --> 00:01:59.520
So the value of the acceleration is positive.
00:02:00.120 --> 00:02:04.320
And this is positive five meters per second squared.
00:02:05.400 --> 00:02:13.120
Very finally, we know that the distance that the object is moving, we’ll call this 𝑠, is 17.1 meters.
00:02:13.720 --> 00:02:16.760
And this distance is a straight line.
00:02:17.680 --> 00:02:25.800
The fact that the object is moving along a straight line is important because it means that it can have a constant acceleration.
00:02:26.640 --> 00:02:30.040
Remember, acceleration is the rate of change of velocity.
00:02:30.600 --> 00:02:33.720
And velocity is speed in a given direction.
00:02:34.280 --> 00:02:39.160
So acceleration doesn’t just mean when you speed up or slow down.
00:02:39.840 --> 00:02:43.640
You can also accelerate if you change direction.
00:02:44.480 --> 00:02:50.080
However, in this case, we’ve got an acceleration which is five meters per second squared.
00:02:50.640 --> 00:02:51.920
So it’s constant.
00:02:52.680 --> 00:02:57.920
And because the object is moving in a straight line, it’s not changing direction either.
00:02:58.520 --> 00:03:01.720
So the acceleration is overall a constant.
00:03:03.120 --> 00:03:12.440
This becomes important because at this point, we can use a set of equations known as the SUVAT equations.
00:03:13.440 --> 00:03:16.880
The SUVAT equations are a set of equations of motion.
00:03:17.400 --> 00:03:23.280
That is, they describe how objects move, provided that the acceleration of the object is constant.
00:03:24.040 --> 00:03:26.800
And as we’ve just seen, it is.
00:03:27.200 --> 00:03:32.240
Which means that we can use the SUVAT equations in this scenario.
00:03:33.080 --> 00:03:50.560
Now, the reason that SUVAT equations are called SUVAT equations is because they deal with quantities, such as the distance travelled, 𝑠, the initial velocity, 𝑢, the final velocity, 𝑣, the acceleration, 𝑎, and the time taken, 𝑡.
00:03:51.840 --> 00:03:55.080
In this case, we don’t have the time taken, 𝑡.
00:03:55.760 --> 00:03:57.000
But that doesn’t matter.
00:03:57.480 --> 00:04:05.240
We need to use the SUVAT equation that deals with these four quantities 𝑢, 𝑣, 𝑎, and 𝑠.
00:04:05.840 --> 00:04:10.840
And that SUVAT equation happens to be: 𝑣 squared is equal to 𝑢 squared plus two 𝑎𝑠.
00:04:11.720 --> 00:04:15.240
Now, in this case, we’re trying to solve for what the initial velocity is.
00:04:15.640 --> 00:04:17.080
We’re trying to solve for 𝑢.
00:04:17.440 --> 00:04:19.840
So we need to rearrange this equation.
00:04:20.800 --> 00:04:24.680
First thing we can do is to subtract two 𝑎𝑠 from both sides.
00:04:25.280 --> 00:04:32.080
This means that two 𝑎𝑠 cancels on the right-hand side, leaving us with 𝑣 squared minus two 𝑎𝑠 is equal to 𝑢 squared.
00:04:32.960 --> 00:04:36.920
Now, what we can do is to take the square root of both sides of the equation.
00:04:37.920 --> 00:04:42.400
On the right-hand side, once again, the squared cancels with the square root.
00:04:42.720 --> 00:04:47.880
And so we find that the square root of 𝑣 squared minus two 𝑎𝑠 is equal to 𝑢.
00:04:49.080 --> 00:05:07.920
At this point, all we need to do is to sub in the values of 𝑣, 𝑎, and 𝑠, which looks something like this: 𝑢 is equal to the square root of 𝑣 squared, which is 14 squared, minus two times 𝑎, which is five, times 𝑠, which is 17.1.
00:05:09.080 --> 00:05:29.120
And since all of the quantities that we’ve used are in their standard units, 𝑣 is in meters per second, 𝑎 is in meters per second squared, and 𝑠 is in meters, the value that we find for 𝑢 is going to be in its standard units.
00:05:29.680 --> 00:05:36.800
Now, 𝑢 is the initial velocity of the object and the standard unit of velocity is meters per second.
00:05:37.400 --> 00:05:40.920
So our answer is going to be in meters per second.
00:05:41.880 --> 00:05:47.360
Plugging this into our calculator, we find that the value of 𝑢 is five meters per second.
00:05:48.200 --> 00:05:50.120
And this is our final answer.
00:05:50.840 --> 00:05:56.080
The object’s initial velocity is five meters per second.