# Vector dynamics question starting from accelaration

In summary, the problem involves finding the time when velocity is zero and the velocity and total distance traveled when t = 11 s. To solve this, the equations for velocity and displacement must be integrated. However, initial conditions must also be taken into account and can be determined from the given information.

## Homework Statement

I took this right out of the text, it is not home work just me trying to get better.

The acceleration of a particle is defined by the relation a = -8 m/s^2
Knowing that x = 20 m when t= 4 m, and that x = 4 m when v = 16 m/s
(a) determine the time when velocity is zero and (b) the velocity and total distance traveled when t = 11 s

## The Attempt at a Solution

My attempt is I know velocity must be the integration of acceleration and displacement the integration of velocity. So I attempted to integrate -8dt 2 times. but when I do that I get x=-4t^2 which does not fit my given when t=4, x=20
Any help would be greatly appreciated, even just pointing me in the right direction

Looks like you need to take initial conditions into account. Remember that when you integrate you have a constant of integration as well, which you can determine if you have initial conditions (which you have).

How do I know which of the conditions to use for the initial conditions?

## 1. How is acceleration related to vector dynamics?

Acceleration is a vector quantity that represents the rate of change of velocity over time. In vector dynamics, acceleration is an important concept as it helps us understand how an object's velocity changes in both magnitude and direction.

## 2. What are some common examples of vector dynamics?

Examples of vector dynamics include the motion of a projectile, the orbit of a planet around a star, and the movement of a car around a circular track. In all of these cases, there is a changing velocity and thus a non-zero acceleration.

## 3. How is vector addition used in vector dynamics?

In vector dynamics, vector addition is used to combine multiple forces acting on an object. This allows us to calculate the resulting acceleration of the object by finding the net force acting on it.

## 4. What is the relationship between velocity and acceleration in vector dynamics?

Velocity and acceleration are closely related in vector dynamics. Acceleration is the derivative of velocity, meaning it is the rate of change of velocity over time. This means that a change in acceleration will result in a corresponding change in velocity, and vice versa.

## 5. How does the direction of acceleration affect an object's motion in vector dynamics?

The direction of acceleration is crucial in determining an object's motion in vector dynamics. If an object experiences a constant acceleration in the same direction as its velocity, it will continue to increase in speed. However, if the acceleration is in the opposite direction to the velocity, the object will slow down. If the acceleration is perpendicular to the velocity, the object will change direction but not speed.

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