# Kinematic Problem: Tangential Acceleration and Radius of Curvature at t=1

• Dell
In summary, the given conversation discusses the motion of a body with equations for acceleration and velocity in terms of time. The tangential acceleration at t=1 is found to be zero due to the velocity being zero at that time. The concept of linear acceleration is also mentioned and the radius of curvature is suggested as a way to further analyze the motion.
Dell
a body moves according to the following:
ay=2-4t
ax=-1
vy=2t-2t2
vx=1-t
x0=2
y0=3

what is the tangential acceleration when t=1?
what is the radius of curvature of the motion when t=1?

aT=$$\vec{a}$$dot$$\vec{v}$$/|v|
at t=1, $$\vec{v}$$=0 so there is no tangential acceleration, how can this be true?

the secon part of the question is also not making sence

ar=v2/r, but here v=0 and ar=3 since there is no aT and ax=-1, ay=-2?

I would like to clarify and provide a response to the given kinematic problem. First of all, the given problem does not provide enough information to accurately determine the tangential acceleration and radius of curvature at t=1. In order to solve for these values, we would need to know the position, velocity, and acceleration of the body at t=1.

Furthermore, the given equations for ay and ax do not match the given initial conditions of x0=2 and y0=3. This suggests that there may be errors or missing information in the given problem.

Assuming that the initial conditions are correct and the equations for ay and ax are meant to represent the acceleration components, we can solve for the tangential acceleration and radius of curvature at t=1 using the equations aT=\vec{a}\cdot\vec{v}/|v| and ar=v^2/r.

At t=1, the velocity components are vx=0 and vy=0, so the magnitude of the velocity, |v|, is also equal to 0. This means that the tangential acceleration, aT, cannot be determined using the given information.

Similarly, the radius of curvature, r, cannot be determined without knowing the velocity and acceleration components at t=1. As mentioned before, the given equations for ay and ax do not match the initial conditions, so it is not possible to accurately determine the radius of curvature at t=1.

In conclusion, the given kinematic problem does not provide enough information to accurately determine the tangential acceleration and radius of curvature at t=1. It is possible that there are errors or missing information in the given problem. Further clarification or additional information is needed to solve for these values.

## What is tangential acceleration?

Tangential acceleration is the rate of change of an object's tangential velocity. It is a measure of how quickly the object's speed is changing as it moves along its curved path.

## How is tangential acceleration related to radius of curvature?

The tangential acceleration at a specific point on a curved path is directly related to the radius of curvature at that point. This means that the smaller the radius of curvature, the greater the tangential acceleration will be at that point.

## How is tangential acceleration calculated?

Tangential acceleration can be calculated using the formula: at = v^2 / r, where v is the tangential velocity and r is the radius of curvature at a specific point on a curved path.

## What are some real-life applications of tangential acceleration?

Tangential acceleration is important in understanding the motion of objects in circular or curved paths, such as vehicles on a curved road or satellites orbiting the Earth. It is also important in analyzing the forces acting on objects during rotational motion.

## How does tangential acceleration differ from centripetal acceleration?

Tangential acceleration and centripetal acceleration are both related to circular motion, but they are different concepts. Tangential acceleration measures the change in tangential velocity, while centripetal acceleration measures the change in direction of an object's velocity, always pointing towards the center of the circular path.

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