# Question why is there a negative sign

• camboguy
In summary, the position of a particle moving along the c axis is given by the equation x = 2+3t-4t^2, with x in meters and t in seconds. To determine its position when it changes direction, we can find the value of t when the velocity is equal to zero, which will be the time when the particle changes direction. To find the velocity when it returns to the position it had at t = 0, we need to use the equation -x = -2-3t+4t^2, which has the negative sign because there is a change in direction at t = 0. The negative sign indicates that the particle is moving in the opposite direction to its initial direction.
camboguy
A particle moves along the c axis. its position is given by the equation x = 2+3t-4t^2, with x in meters and t in seconds. Determine (a) its position when it changes direction and )b) its velocity when it returns to the position it had at t = 0.

i understand how to get (a) but for (b) I am confused why in the solution they put -x = -2-3t+4t^2 why is the negative there, i understand there is a change in direction at 0, I am confused why the negative sign is there can you give me a clear and understanding reasoning. thank you.

I have no clue. They just randomly decided to flip the signs on everything, it looks like =/

The negative sign in the solution for (b) represents the direction of motion of the particle. In the given equation, the coefficient of t^2 is negative, which means that the particle is moving in the negative direction along the c axis. This is because as t increases, the value of x decreases, indicating that the particle is moving in the opposite direction of the positive c axis.

When the particle returns to its initial position at t = 0, its velocity will also be in the opposite direction of its initial velocity, which is why the negative sign is included in the solution. This is a common convention in physics, where negative values represent motion in the opposite direction.

In summary, the negative sign in the solution represents the direction of motion of the particle and is necessary to accurately describe its velocity when it returns to its initial position.

## 1. Why do negative signs exist?

Negative signs exist in mathematics and science because they represent a negative quantity or direction. In other words, they indicate a decrease or opposite direction from a given reference point.

## 2. How do negative signs affect calculations?

Negative signs affect calculations by indicating a subtraction or opposite direction from a given reference point. They can change the overall value or direction of a calculation, so it is important to pay attention to them in equations.

## 3. Can there be negative numbers in real life?

Yes, there can be negative numbers in real life. For example, a person's bank account balance can be negative if they owe money. Negative temperatures and sea levels also exist in real life. Negative numbers are a useful tool for representing values that are less than zero.

## 4. What is the difference between a negative sign and a minus sign?

A negative sign and a minus sign are often used interchangeably, but they have different meanings in mathematics. A negative sign indicates a negative quantity or direction, while a minus sign is used to indicate subtraction in equations.

## 5. Can a negative number be squared?

Yes, a negative number can be squared. When a negative number is squared, the result will be a positive number. For example, (-2)^2 = 4. This is because multiplying a negative number by itself will always result in a positive number.

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