# Instantaneous velocity problem

Describe the motion of an object that is initially traveling with a constant velocity and then receives an acceleration of constant magnitude a) in a direction parallel to the initial velocity, b) in a direction perpendicular to the initial velocity, and c) that is always perpendicular to the instantaneous velocity or direction of motion.

a) Same direction, and would speed up

b) Object would slow down - Something is going forward and has a instantaneous acceleration against it, it would seem to slow down?

c) Object would stop - If something is constantly pressing down on something going forward, it cannot have forward motion, if the magnitude of both are the same. But then again this does not make sense with gravity.

I drew a picture, but with arrows. Here is what my book says, "If an object is initially moving with a constant velocity and suddenly experiences an acceleration in the direction of the velocity or opposite to it, it will continue in a straight line path, either speeding up or slowing down, respectively."
Am I way off? Do you mind explaining this to me?

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CompuChip
Homework Helper
Hi, welcome to PF.
You're correct about a), but I think that b) and c) are not the right answer. Can you explain your reasoning (preferably for all three of them).

By the way, did you try drawing a picture? Because from your answers I have the feeling that you don't quite understand the situation. But that's just guessing at the problem, you better explain it After rereading the caption in the book, im not so sure it would slow down or stop. The perpendicular may have no effect on the motion of the object at all.

Doc Al
Mentor
Describe the motion of an object that is initially traveling with a constant velocity and then receives an acceleration of constant magnitude a) in a direction parallel to the initial velocity, b) in a direction perpendicular to the initial velocity, and c) that is always perpendicular to the instantaneous velocity or direction of motion.

a) Same direction, and would speed up
Assuming that "parallel" means in the same direction (and not backwards, which is anti-parallel), then you are correct.

b) Object would slow down - Something is going forward and has a instantaneous acceleration against it, it would seem to slow down?
No. Can you think of example of this kind of situation? Here's one: You throw a ball horizontally off of a cliff. The initial velocity is horizontal, but gravity acts vertically. What happens to the speed and direction of motion of the ball?

c) Object would stop - If something is constantly pressing down on something going forward, it cannot have forward motion, if the magnitude of both are the same. But then again this does not make sense with gravity.
No. Here's a hint for this one: In order for an acceleration to change the speed of an object, it must have a component in the direction of the velocity. Realize that velocity, being a vector, can change in either of two ways: its magnitude can change (speed up or slow down) or its direction can change.