# Questions pertaining to constant velocity + acceleration and relative motion

1) In the following four scenarios, determine the sign of the ball’s velocity and acceleration.

Up is positive. The ball is thrown straight up. (Velocity is positive, Acceleration is negative)
Up is positive. The ball is dropped straight down. (Velocity is negative, Acceleration is negative)
Down is positive. The ball is thrown straight up. (Velocity is negative, Acceleration is positive)
Down is positive. The ball is dropped straight down (Velocity is positive, Acceleration is positive)

My answers are in parenthesis...but I'm not entirely 100% sure why these answers are what they are. A little clarification would be nice.

Next question pertains to relative motion:

You are in a car traveling south at 50 mph. What is your speed relative to:
A car traveling south at 50 mph? Zero (this one was obvious)
A car traveling south at 25 mph? 25...?
A car traveling north at 50 mph? 0?
A car traveling north at 25 mph? 75...?

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My answers are in parenthesis...but I'm not entirely 100% sure why these answers are what they are. A little clarification would be nice.
Your answers are correct. If we choose some direction in space, then anything going or acting in that direction is "positive", and anything in the opposite direction is "negative".

You are in a car traveling south at 50 mph. What is your speed relative to:
A car traveling south at 50 mph? Zero (this one was obvious)
A car traveling south at 25 mph? 25...?
A car traveling north at 50 mph? 0?
Imagine that these two cars meet (at the opposite sides of the road, so there is no collision) at some moment in time. If their relative speed is zero, then for any duration of time their relative distance must also be zero. Which is clearly not the case. How does their relative distance changes with time? Can you deduce their relative speed from how relative distance chages?
A car traveling north at 25 mph? 75...?