# Velocity with changing direction

• AshleyJayda
In summary, the particle in question has a constant acceleration and experiences a change in direction after 1s, with an initial velocity of 5m/s and a final velocity of -5m/s. The displacement from its original position at 1s can be solved using the equation x = x0 + v0t + ½ at2 and another equation. The direction chosen as plus or minus does not affect the solution, as long as it is consistent.
AshleyJayda
A particle moving at 5m/s reverses its direction in 1s to move at 5m/s in the opposite direction. If its acceleration is constant, what is its displacement from its original position at 1s?

I know how to solve the equation:
1) x = x0 + v0t + ½ at2
2) a is unknown therefore solve for a

My question is how do you know the the initial velocity is negative? I would say the initial velocity is 5m/s and after it changes direction velocity is then -5m/s. The solution says the opposite, i.e. initial velocity is -5m/s and final velocity is 5m/s. How do you know? Is there some hard and fast rule I am unaware of?

It doesn't make any difference which direction you choose as plus or minus, as long as you are consistent in your sign convention. Also, you're going to need another equation in addition to (or in substitution of) the one you have shown to get the answer. No matter what, the plus and minus sign will wear down the best of us.

I understand your confusion about the initial velocity being negative. However, in this scenario, we are dealing with a velocity that is changing direction, which means it is also changing its sign. When we say that the initial velocity is -5m/s, it simply means that the particle is moving in the opposite direction with the same speed. This is a common convention used in physics to indicate the direction of motion.

To better understand this, let's look at the velocity-time graph of the particle's motion. The initial velocity of 5m/s would be represented by a positive slope on the graph, indicating motion in the positive direction. When the direction is reversed, the slope becomes negative, indicating motion in the negative direction. This is why we use a negative sign to represent the initial velocity in this scenario.

In terms of solving the equation, it doesn't matter whether we use a positive or negative sign for the initial velocity, as long as we are consistent throughout the calculation. So, in your approach, if you take the initial velocity as 5m/s, then the final velocity would also be -5m/s, and the displacement calculated would be the same.

I hope this clarifies your doubt. In summary, there is no hard and fast rule about the sign of the initial velocity, it is just a convention used in physics to indicate the direction of motion.

## 1. What is velocity with changing direction?

Velocity with changing direction is the measurement of the rate at which an object changes its position in a specific direction. It takes into account both the speed of the object and the direction in which it is moving.

## 2. How is velocity with changing direction calculated?

Velocity with changing direction is calculated by dividing the displacement of an object by the time it took to cover that distance. It is a vector quantity, meaning it has both magnitude (speed) and direction.

## 3. What is the difference between velocity and speed with changing direction?

The main difference between velocity and speed with changing direction lies in the direction component. While speed only measures the rate of change of an object's position, velocity takes into account the direction in which the object is moving.

## 4. Can velocity with changing direction be negative?

Yes, velocity with changing direction can be negative. This indicates that the object is moving in the opposite direction of the chosen reference point. For example, if a car is moving east, its velocity would be positive, but if it turns around and starts moving west, its velocity would become negative.

## 5. How does acceleration affect velocity with changing direction?

Acceleration affects velocity with changing direction by changing the magnitude and/or direction of the velocity. If an object is accelerating, its velocity will change over time, either by increasing or decreasing in speed and/or changing its direction of motion.

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