2) This question asks us to find the time when the object described with the position versus time graph has the greatest speed. This question isn't too hard if we read it correctly. Some people may read "greatest" and immediately look for the greatest value on the graph. This would result in time t = 9. However, this is the greatest displacement from origin. We want to find the greatest speed.
So how do we do this? Well, if you've taken calculus, you would know that we can find the speed by looking at the instantaneous slope of the position and time graph. For those that haven't taken calculus, we are essentially looking for the slope of the tangent line.
We can draw the tangent lines out to make this easily apparent.
Remember though, that we don't care about the sign of the slope. We are asked to find the greatest speed, so we only care about the magnitude of the slope.
We see that at t = 3 seconds, the slope is the greatest.
Answer: A
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