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I am trying to understand net force intuitively and this is what I think.

If a net force is towards the positive $x$ direction, which of the following is true ?

a) It can be moving in the negative $x$ direction

b) It can be speeding up

c) It can be slowing down

d) It can be moving in the positive $y$ direction

a) No, because if an object is moving towards the left, $x_f-x_i$ is negative, so the velocity is negative as well as the acceleration. So, impossible.

b) Yes. as a matter of fact it has to because positive acceleration means speeding up.

c) No. Same reason as b.

d) No, because the y-direction is perpendicular to the x.

I got this problem wrong and I don't think I am really understanding acceleration. Can someone help me out ?

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4 Answers 4

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If a net force is towards the positive x direction,

then the $x$ component of velocity of the object is increasing; period.

Now, knowing this, are any of the statements (a) through (d) true?

a) It can be moving in the negative x direction

Sure, it could be moving in the negative $x$ direction. All that is required is that the velocity is becoming less negative (increasing), i.e., that the acceleration is in the positive $x$ direction.

b) It can be speeding up

Sure, speed is the magnitude of the velocity. So, it could be speeding up if it were moving in the positive $x$ direction.

c) It can be slowing down

Sure, speed is the magnitude of the velocity. So, it could be slowing down up if it were moving in the negative $x$ direction.

d) It can be moving in the positive y direction

Sure and this motion would be completely unaffected by the net force in the positive x direction.

Acceleration is the rate of change in velocity. If one tells you that the velocity is changing but doesn't specify what the velocity is, you don't know anything about the velocity, only its rate of change.

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The only thing that a net force in the positive $x$ direction means is that the net acceleration is in that direction. It tells you nothing about its position or velocity.

a) Imagine placing the $x$-axis vertically and letting the positive $x$ direction be downward. Now imagine that the constant force is gravity and the particle is a ball.

If you throw the ball upwards, it has a negative velocity (so it is moving in the negative $x$ direction) but it has a positive acceleration.

b and c) These relate directly to the analogy described above. An object moving upward experiences slowing down (an acceleration opposite the direction as velocity), while an object moving downward experiences speeding up (an acceleration in the same direction as velocity).

d) A net force in the $x$ direction will have no effect on velocities in the $y$ direction, so the particle's motion in the $y$ direction is independent of its motion in the $x$ direction. The particle can be moving in the $y$ direction.

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  • $\begingroup$ -1: Wrong on d). A net force in only the x-direction does not say ANYthing about a constant velocity in the y-direction. $\endgroup$
    – Danu
    Commented Dec 5, 2013 at 23:42
  • $\begingroup$ You're right. I misread d as "can be accelerating...". Corrected. $\endgroup$
    – xish
    Commented Dec 5, 2013 at 23:43
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a), b), c), d) All yes. Imagine a ball that is moving at 10 meters per second to the left (negative x direction). Now, a force in the positive x-direction will slow it down initially, and finally make it go to the right, constantly accelerating to the right. This is all independent of the y-direction, in which it might also be moving. A force in the x-direction doesn't tell us that the ball is not moving in the y-direction.

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To complement the other answers, there could still be an alternative e) in which the object may be momentarily stopped in axis x after having completely slowed down the velocity in the negative direction of the x axis, and for a moment had zero velocity before changing from to the negative direction of x.

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