Question

at what point on the position-time graph shown is the object's instantaneous velocity smallest

Answer 1

@Directrix @kropot72

Answer 2

Look at the graph.

What is going on to the immediate left of point D? What is going on to the immediate right of point D? By "going on," I mean with regard to velocity.

Answer 3

20,50?

Answer 4

D=50/20=2.5

Answer 5

nvm I figured it out I just had to do the velocity formula which would give me F :)

Answer 6

As best I remember, at point D, the instantaneous velocity is zero.

This is a conceptual rather than computational question, to my thinking.

Answer 7

but velocity is m/s therefore D would be the biggest point

Answer 8

@daniellelovee
Velocity is dy/dx, or the rate of change of x.
On a "curved line" velocity-time graph, velocity is the slope of the tangent line.
The slope of the tangent line is zero (i.e. tangent line is horizontal) at both D and F, which means that the velocities are both zero.
So both D and F are valid answers for zero instanteneous velocity, and both are correct answers IF the question asked for the minimum \(speed\).

Since velocity is a signed quantity, so the smallest velocity will mean the "most negative velocity", or the "most negative" slope of the tangent line, which I believe (visually) occurs at E (assuming it is not a kink.)