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Classical Mechanics Level 2

If the Displacement vs. Time (Displacement on $y$ -axis, Time on $x$ -axis) graph of a ball has its vertex at $y=10$ and its directrix at $y=12$ , then the Speed vs. Time (Speed on $y$ -axis, Time on $x$ -axis) would be a _ __ function (ignore air resistance).

Positive Linear Positive Quadratic Negative Absolute Value Positive Absolute Value Negative Exponential Negative Linear Negative Quadratic Positive Exponential

1 solution

Yashas Ravi
Jun 29, 2019

If the Directrix is above the Vertex, then it is a Negative-Quadratic Displacement vs. Time graph. The slope of the line tangent to the graph decreases until the vertex, and then increases after the vertex. In a Speed vs. Time graph, this translates to a line with negative slope before the $x$ -coordinate of the vertex, and then a line with positive slope after the $x$ -coordinate of the vertex. This is basically a positive absolute function, which looks like a "V" when graphed.

The slope of the tangent to the curve becomes negative after the vertex. Hence the slope decreases monotonically. Second derivative of the displacement with respect to time is negative definite.

A Former Brilliant Member - 1 year, 11 months ago

Wouldn't the Slope of the tangent line would be velocity? Velocity is a vector, meaning it can be negative. Since we are dealing with speed, it is a scalar quantity and cannot be negative. Thus, wouldn't it be the absolute value of the slope before and after the vertex? Thanks!

Yashas Ravi - 1 year, 11 months ago

You wrote velocity Vs time in the problem.

A Former Brilliant Member - 1 year, 11 months ago

@A Former Brilliant Member – Oh...I first wrote speed, then after reading your post I got confused and changed it to velocity and then forgot to change it back to speed...oops!

Yashas Ravi - 1 year, 11 months ago

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