# Solving Particle Trajectory: Speed & Direction at t=4.5s

• jimmyv12
In summary, the particle's trajectory is described by x=((1/2)t^3 - 2t^2) and y=((1/2)t^2-2t) where t is in s. To find the particle's speed at t=4.5 s, take the derivatives of both x and y and use the formula sqrt(x^2+y^2). To find the direction of motion, use the formula y=cos^-1(x/v) where v is the speed calculated in the first step.
jimmyv12
A particle's trajectory is described by x=((1/2)t^3 - 2t^2) and y=((1/2)t^2-2t) , where t is in s.

What is the particle's speed at t= 4.5 s?
What is the particle's direction of motion, measured as an angle from the x-axis, at t=4.5 s?

I keep geting the wrong answers >:0 , how do I go about solving this?

How did you try solving this? Show us so we can explain where you went wrong.

Take the derivative of both.

Then solve for t = 4.5s, us these vector components to find the angle.

Last edited:
Alright, so i don't know why I wasnt getting the right answer before(i was taking the derivatives), but I took the derivatives for x and y, then used the sqrt(x^2+y^2) to get part one. Then y=cos^-1(x/v) for part two.

## 1. What is particle trajectory?

Particle trajectory refers to the path that a particle takes as it moves through space. It includes information about the particle's speed, direction, and position at any given time.

## 2. How is particle trajectory calculated?

Particle trajectory is calculated using mathematical equations and principles, such as Newton's laws of motion and calculus. It involves determining the particle's initial conditions, such as its velocity and position, and using equations to predict its future position at a specific time.

## 3. What is the importance of determining particle trajectory?

Determining particle trajectory can provide valuable information about the behavior and properties of particles. It can also help in understanding and predicting the movement of particles in various systems, such as in fluid dynamics or particle accelerators.

## 4. How is speed and direction of a particle determined at a specific time?

The speed and direction of a particle at a specific time can be determined by using the particle's trajectory equations and plugging in the time value. This will give the velocity vector, which includes both the speed and direction of the particle at that moment in time.

## 5. How can the speed and direction of a particle at t=4.5s be used in scientific research?

The speed and direction of a particle at a specific time, such as t=4.5s, can be used to analyze and understand the behavior of particles in various systems. It can also be used to make predictions about the future movement of particles and to validate theoretical models and equations. This information can be crucial in fields such as fluid dynamics, particle physics, and astrophysics.

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