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How to determine the direction of instantaneous acceleration in a 2D motion?

Discussion in 'Physics' started by π times e, Oct 8, 2018.

  1. π times e

    π times e Guest

    How do we determine the direction of instantaneous acceleration when the body is moving in a plane (or a 3D space)? This question has been truly bothering me for nearly two weeks. I looked it up, found a similar post, but that didn't really clear up my doubts, so I decided to put it up.

    Let's get to the point. I do understand the direction of acceleration (average or instantaneous) is along the direction of "change in velocity" over a time interval t. And it's relatively much more easy, to find the direction of that "change in velocity" (vector addition/subtraction), if the time interval over which the change takes place is significantly larger, say 5 seconds, 10 seconds...etc. But it gets much more challenging to determine this direction when the time interval becomes infinitesimally small, i.e when it approaches zero. Let's say for example, a body is moving along a curve, and it's trajectory equation is $y = x²$. It means the body is moving along a parabolic path. What I know is, the body's instantaneous velocity at any point, is along the tangent to the curve at that point. But,

    1. How do we find the direction of its instantaneous acceleration at that point, if all we're given is its trajectory equation?

    And

    1. If we differentiate its trajectory equation partially wrt time, and plot its Vy vs Vx relation, what does the tangent at any point to this Vy vs Vx curve give? Does the slope of a Vy vs Vx curve have any physical meaning?

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