WEBVTT
00:00:02.180 --> 00:00:06.680
Which of the following formulas correctly relates time, distance, and speed?
00:00:07.450 --> 00:00:22.940
(A) ๐ equals one over ๐๐ก, (B) ๐ equals ๐ minus ๐ก, (C) ๐ equals ๐ plus ๐ก, (D) ๐ equals ๐ multiplied by ๐ก, (E) ๐ equals ๐ over ๐ก.
00:00:25.120 --> 00:00:34.740
Okay, so in this question, weโre presented with five different possible formulas and asked which of them correctly relates the three quantities time, distance, and speed.
00:00:36.430 --> 00:00:44.050
We have time, which is labeled ๐ก; distance, which is labeled ๐; and speed, which is labeled ๐ .
00:00:45.520 --> 00:00:50.920
Now, whenever weโre trying to work out if a formula is correct, it can be helpful to look at the units.
00:00:52.420 --> 00:00:59.690
In order for a particular formula to be correct, the units of the left-hand side of that formula must equal the units of the right-hand side.
00:01:01.180 --> 00:01:08.670
In other words, if the left- and right-hand sides of a formula have different units to each other, then we know that that formula cannot be correct.
00:01:10.160 --> 00:01:17.400
To see why this is, remember that the equal sign in an equation means that the left-hand side is equal to the right-hand side.
00:01:18.040 --> 00:01:23.510
If those two sides have different units, we cannot compare them in a meaningful way to say that they are equal.
00:01:25.190 --> 00:01:29.710
For example, we could say that three apples is equal to two apples plus one apple.
00:01:31.200 --> 00:01:35.680
In this case, the units on both sides of the equation are units of apples.
00:01:37.210 --> 00:01:42.320
So the units on both sides of this equation agree with each other, and this equation makes sense.
00:01:44.010 --> 00:01:57.270
But if instead, on the left-hand side, we had three oranges, then we now have an equation where the right-hand side has units of apples and the left-hand side has different units, units of oranges.
00:01:58.590 --> 00:02:04.580
And it should be clear that we cannot compare a quantity in units of oranges to a quantity in units of apples.
00:02:05.810 --> 00:02:07.810
So this equation makes no sense.
00:02:10.010 --> 00:02:19.950
Since we cannot compare quantities with different units in this way, this also means that we cannot add or subtract two quantities with different units to each other.
00:02:21.600 --> 00:02:30.660
If we go back to our analogy with fruit, we can add two apples to one apple and get a result in units of apples, in this case, three of them.
00:02:32.390 --> 00:02:37.280
But if we try to add two apples to one orange, then we see that this doesnโt make any sense.
00:02:37.360 --> 00:02:41.680
We donโt know how to add together these two quantities because they have different units.
00:02:43.400 --> 00:02:51.130
So weโve now identified a couple of things that we can check with the units of our quantities in order to see if a particular formula could be correct.
00:02:52.710 --> 00:03:05.990
So now letโs work through our list of potential formulas relating time, distance, and speed that were given in the question to see if any of them fulfill the necessary requirements on the units of the quantities in order to be correct.
00:03:07.660 --> 00:03:12.700
First off, we need to identify the units of each of the quantities involved in these equations.
00:03:13.790 --> 00:03:26.640
If we work in SI units, then we have that the quantity time, if we work in SI units, then we have that the quantity time with symbol ๐ก has units of seconds.
00:03:27.680 --> 00:03:33.110
We have that distance with a symbol ๐ has units of meters.
00:03:34.040 --> 00:03:41.320
And finally, we have that speed with a symbol ๐ has units of meters per second.
00:03:42.390 --> 00:03:47.010
Okay, looking at the potential formulas that we are given, letโs start with option (A).
00:03:48.090 --> 00:03:53.170
This formula says that ๐ is equal to one divided by ๐ times ๐ก.
00:03:54.640 --> 00:03:57.790
So does this formula make sense in terms of the units?
00:03:59.150 --> 00:04:02.000
If we look at the left-hand side, we have speed.
00:04:02.490 --> 00:04:06.820
And if we look in our table, we see that speed has units of meters per second.
00:04:07.990 --> 00:04:17.580
Now looking at the right-hand side of the formula, we have one divided by distance, which has units of meters, and time, which has units of seconds.
00:04:18.440 --> 00:04:25.780
And so we have that the units are one divided by units of meters multiplied by units of seconds.
00:04:27.350 --> 00:04:29.250
So can this formula be correct?
00:04:30.250 --> 00:04:41.450
Well, if we write this a little more clearly, we have that the left-hand side has units of meters divided by seconds, while the right-hand side has units of one divided by meters multiplied by seconds.
00:04:43.400 --> 00:04:51.420
And since the units on the left-hand side do not equal the units on the right-hand side, then we have not met our first requirement on the units of the formula.
00:04:52.910 --> 00:04:55.840
And so we have that option (A) cannot be correct.
00:04:57.000 --> 00:04:58.630
Now letโs look at option (B).
00:04:59.810 --> 00:05:05.530
This formula says that distance ๐ is equal to speed ๐ minus time ๐ก.
00:05:06.960 --> 00:05:18.840
If we look at the right-hand side of this formula in terms of the units, we see that we have speed, a quantity with units of meters per second, minus time, a quantity with units of seconds.
00:05:19.920 --> 00:05:25.330
And so we are trying to subtract one quantity from another when those two quantities have different units.
00:05:26.520 --> 00:05:30.140
So this contradicts our second requirement for the units of a formula.
00:05:31.170 --> 00:05:33.610
And so option (B) cannot be correct.
00:05:34.880 --> 00:05:36.490
Now, letโs look at option (C).
00:05:37.700 --> 00:05:44.030
We see that this formula is telling us that speed ๐ is equal to distance ๐ plus time ๐ก.
00:05:45.660 --> 00:05:55.540
And if we look at the units on the right-hand side of this equation, we see that weโre trying to add a distance with units of meters to a time with units of seconds.
00:05:56.660 --> 00:06:04.390
And since weโre trying to add together two quantities with different units to each other, this doesnโt meet our second requirement on the units of a formula.
00:06:06.580 --> 00:06:09.260
So we know that option (C) canโt be correct.
00:06:10.670 --> 00:06:20.580
If we now consider option (D), we see that this formula is telling us that speed ๐ is equal to distance ๐ multiplied by time ๐ก.
00:06:21.960 --> 00:06:28.930
If we look at this formula in terms of its units, we see that on the left-hand side we have speed with units of meters per second.
00:06:30.020 --> 00:06:37.110
Meanwhile, on the right-hand side, we have distance with units of meters multiplied by time with units of seconds.
00:06:39.000 --> 00:06:46.090
So on the left-hand side, we have units of meters divided by seconds, while on the right-hand side, we have meters multiplied by seconds.
00:06:47.100 --> 00:06:50.610
So the units on the two sides of the formula donโt agree with each other.
00:06:51.530 --> 00:06:56.610
And our first requirement on the units of a formula is not met by the formula in option (D).
00:06:57.870 --> 00:07:00.410
And so we know that this cannot be the correct answer.
00:07:01.910 --> 00:07:04.600
This leaves us with one last formula to consider.
00:07:04.920 --> 00:07:06.020
And thatโs option (E).
00:07:07.480 --> 00:07:13.100
This formula states that speed ๐ is equal to distance ๐ divided by time ๐ก.
00:07:14.930 --> 00:07:23.600
Now at this point, we could say that this must be the correct answer by process of elimination since weโve already shown that all of the other answers cannot be correct.
00:07:25.110 --> 00:07:29.620
But in order to be thorough, we should check that the units do make sense in this case.
00:07:31.040 --> 00:07:36.830
If we look at the left-hand side of this formula, we see that we have speed with units of meters per second.
00:07:38.060 --> 00:07:44.260
And on the right-hand side, we have distance with units of meters divided by time with units of seconds.
00:07:45.310 --> 00:07:48.920
On the left-hand side of this, we have units of meters per second.
00:07:50.020 --> 00:07:56.430
Now units of meters per second is nothing more than the fraction units of meters divided by units of seconds.
00:07:58.190 --> 00:08:02.680
And so the units on the left- and the right-hand side of this formula do agree with each other.
00:08:03.920 --> 00:08:07.720
And so this formula meets our requirements that we have for the units.
00:08:09.600 --> 00:08:19.560
And so we have our answer that the formula that correctly relates time, distance, and speed is given by option (E), ๐ equals ๐ divided by ๐ก.