Question Video: Understanding Changes in Velocity Science • Third Year of Preparatory School

Video Transcript

An object is moving northward at a speed of two meters per second. 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? (A) The object is moving northward. (B) The object is not moving. (C) The object is moving southward.

When an object decreases its velocity in the direction that the object is traveling in, one of these three things must happen. The object continues moving in the same direction but at a decreased speed. Two, the object could come to rest. Three, the object reverses the direction in which it moves. Let’s say that the object in this example has an initial velocity that we’ll call 𝑣 sub 𝑖. We can call the change in the object’s speed ∆𝑣 written like this. Lastly, let’s say that the final velocity of the object is 𝑣 sub 𝑓. For any values of these variables, it is true that 𝑣 sub 𝑓 equals 𝑣 sub 𝑖 plus ∆𝑣.

Recall that the change of velocity of the object is in the opposite direction to the initial velocity of the object. If we define 𝑣 sub 𝑖 as positive, ∆𝑣 must be negative as it is in the opposite direction to 𝑣 sub 𝑖. Since 𝑣 sub 𝑖 is positive and ∆𝑣 is negative, we can say that if the magnitude of 𝑣 sub 𝑖 is greater than the magnitude of ∆𝑣, 𝑣 sub 𝑓 is greater than zero. This means that the object continues moving in the same direction but at a decreased speed. It’s also possible that the magnitude of 𝑣 sub 𝑖 equals the magnitude of ∆𝑣, in which case 𝑣 sub 𝑓 equals zero, telling us the object has stopped moving. And lastly, if the magnitude of 𝑣 sub 𝑖 is less than that of ∆𝑣, 𝑣 sub 𝑓 is negative, which means the object reverses direction.

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. So that means the magnitude of 𝑣 sub 𝑖 is less than the magnitude of ∆𝑣. Therefore, 𝑣 sub 𝑓 is less than zero, and the object reverses the direction in which it moves. The object is initially traveling northward. And so when it reverses direction, it must start traveling southward. Therefore, the correct answer is (C). The object is moving southward.