Questions pertaining to constant velocity + acceleration and relative motion

In summary, the ball's velocity and acceleration have different signs depending on the direction in which it is thrown or dropped. If the ball is thrown up, the velocity is positive and the acceleration is negative. If the ball is dropped down, both the velocity and acceleration are negative. If the ball is thrown down, the velocity is negative and the acceleration is positive. And if the ball is dropped up, both the velocity and acceleration are positive. In terms of relative motion, your speed in a car traveling south at 50 mph is zero relative to another car traveling south at the same speed. Your speed is 25 mph relative to a car traveling south at 25 mph, and it is 75 mph relative to a car traveling north at
  • #1
Xelb
20
0
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...?
A stationary car on the side of the road? I really not sure about this...
 
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  • #2
Xelb said:
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...?

Answering previous question, you should be able to answer these, too.

A stationary car on the side of the road? I really not sure about this...

What is 50 mph of your car relative to?
 

Related to Questions pertaining to constant velocity + acceleration and relative motion

1. What is constant velocity and how is it different from constant acceleration?

Constant velocity refers to an object moving at a consistent speed in a straight line, without changing direction. Constant acceleration, on the other hand, refers to an object changing its speed and/or direction at a constant rate over time. In other words, constant velocity does not involve any changes in speed or direction, while constant acceleration does.

2. How are constant velocity and acceleration related to each other?

Constant velocity and acceleration are related through the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. This equation shows that constant acceleration can result in a change in velocity, but constant velocity will not result in any changes.

3. How does relative motion affect constant velocity and acceleration?

Relative motion refers to the movement of an object in relation to another object. In terms of constant velocity and acceleration, relative motion can cause changes in an object's speed and direction, which can affect its velocity and acceleration. For example, if an object is moving at a constant velocity, but another object is moving towards it, the relative motion between the two objects can result in a change in velocity for the first object.

4. Can an object have both constant velocity and constant acceleration at the same time?

No, an object cannot have both constant velocity and constant acceleration at the same time. Constant velocity means there is no change in speed or direction, while constant acceleration means there is a change in speed and/or direction. These two concepts are contradictory and cannot occur simultaneously.

5. How do we calculate the displacement of an object with constant velocity and constant acceleration?

To calculate the displacement of an object with constant velocity, we use the formula s = ut, where s is the displacement, u is the initial velocity, and t is the time. For an object with constant acceleration, we use the formula s = ut + 1/2at^2, where a is the acceleration. These equations allow us to calculate the displacement of an object based on its initial conditions and the time elapsed.

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