How do you do B,C,D? (Physics/Velocity)

enter image source here

1 Answer
Feb 12, 2018

See below

Explanation:

The speed of a particle is given by the slope of the x vs t curve - the steeper the curve, the more the position changes for the same change in time.

enter image source here

b) At the intersection marked in red, B's xt graph is steeper, so B is moving faster. At the other intersection, marked blue - A is moving faster.

c) Somewhere in between these two times the tangent to B's xt curve is parallel to A's (the blue straight line in the figure above) - this is when they share a common velocity. That there is such a point is a consequence of what is called the means value theorem of calculus.

d) The slope of B's xt curve is easily seen to decrease over time - option (ii) is the correct one.