WEBVTT 00:00:01.550 --> 00:00:05.050 An object is moving northward at a speed of two meters per second. 00:00:05.430 --> 00:00:14.210 If the object decreases its velocity in the northward direction by three meters per second, which of the following correctly describes the direction in which the object is now moving? 00:00:14.490 --> 00:00:16.580 (A) The object is moving northward. 00:00:16.900 --> 00:00:18.720 (B) The object is not moving. 00:00:18.900 --> 00:00:20.940 (C) The object is moving southward. 00:00:21.160 --> 00:00:27.700 When an object decreases its velocity in the direction that the object is traveling in, one of these three things must happen. 00:00:27.870 --> 00:00:32.110 The object continues moving in the same direction but at a decreased speed. 00:00:32.350 --> 00:00:34.480 Two, the object could come to rest. 00:00:34.660 --> 00:00:37.890 Three, the object reverses the direction in which it moves. 00:00:38.120 --> 00:00:42.610 Let’s say that the object in this example has an initial velocity that we’ll call 𝑣 sub 𝑖. 00:00:42.820 --> 00:00:46.670 We can call the change in the object’s speed βˆ†π‘£ written like this. 00:00:46.900 --> 00:00:50.520 Lastly, let’s say that the final velocity of the object is 𝑣 sub 𝑓. 00:00:50.790 --> 00:00:56.680 For any values of these variables, it is true that 𝑣 sub 𝑓 equals 𝑣 sub 𝑖 plus βˆ†π‘£. 00:00:56.980 --> 00:01:02.470 Recall that the change of velocity of the object is in the opposite direction to the initial velocity of the object. 00:01:02.700 --> 00:01:09.400 If we define 𝑣 sub 𝑖 as positive, βˆ†π‘£ must be negative as it is in the opposite direction to 𝑣 sub 𝑖. 00:01:09.620 --> 00:01:19.100 Since 𝑣 sub 𝑖 is positive and βˆ†π‘£ is negative, we can say that if the magnitude of 𝑣 sub 𝑖 is greater than the magnitude of βˆ†π‘£, 𝑣 sub 𝑓 is greater than zero. 00:01:19.360 --> 00:01:24.010 This means that the object continues moving in the same direction but at a decreased speed. 00:01:24.330 --> 00:01:33.370 It’s also possible that the magnitude of 𝑣 sub 𝑖 equals the magnitude of βˆ†π‘£, in which case 𝑣 sub 𝑓 equals zero, telling us the object has stopped moving. 00:01:33.640 --> 00:01:41.240 And lastly, if the magnitude of 𝑣 sub 𝑖 is less than that of βˆ†π‘£, 𝑣 sub 𝑓 is negative, which means the object reverses direction. 00:01:41.470 --> 00:01:48.620 In this question, the initial velocity has a magnitude of two meters per second and the decrease in velocity has a magnitude of three meters per second. 00:01:48.830 --> 00:01:53.230 So that means the magnitude of 𝑣 sub 𝑖 is less than the magnitude of βˆ†π‘£. 00:01:53.450 --> 00:01:58.700 Therefore, 𝑣 sub 𝑓 is less than zero, and the object reverses the direction in which it moves. 00:01:58.890 --> 00:02:01.170 The object is initially traveling northward. 00:02:01.290 --> 00:02:04.800 And so when it reverses direction, it must start traveling southward. 00:02:05.030 --> 00:02:07.360 Therefore, the correct answer is (C). 00:02:07.560 --> 00:02:09.650 The object is moving southward.