# Tangential and Radial Acceleration problem

• xChrix
In summary, the locomotive is traveling at a speed of approximately 38.2 m/s at the instant when its total acceleration is 0.680 m/s^2 and its tangential acceleration is 0.440 m/s^2. Using the equations for radial and tangential acceleration, the tangential velocity can be calculated by taking the square root of the sum of the squares of the two accelerations. However, the problem only provides the tangential and total accelerations, so the equation needs to be rearranged to solve for the tangential velocity. By doing so, the locomotive's speed can be determined at the given instant.
xChrix

## Homework Statement

As a locomotive rounds a circular curve of radius 1.80 km, its speed is increasing at a rate of 0.440 m/s2. An instrument in the cab (an accelerometer) indicates that the magnitude of the locomotive's total acceleration at a particular instant is 0.680 m/s2. What is the locomotive's speed at that instant?

at = 0.440 m/s^2
a = 0.680 m/s^2
r = 1800 m

## Homework Equations

a = sqrt(aradial^2 + atangential^2) (1)

ar = -[(v^2)/r] (2)

## The Attempt at a Solution

ar = sqrt(0.440^2 + 0.680^2)

ar= 0.80993

0.80993 = -[v^2 divided by 1800 m]

-38.2 But it is showing up in my online assignment that is it wrong :(

Welcome to PF.

I think you almost have it.

It's just that you maybe have switched the sense of what the problem tells you.

You have 2 accelerations as you recognized. Tangential acceleration and Centripetal (Radial).

And the magnitude of their relationship taken together is as I think you figured Radial2 + Tangential2 = Total2

So far so good. But in the statement of the problem they tell you the Tangential and they tell you the Total, but not the Radial. That's what you need to figure the Tangential velocity.

Just change the way you figured it.

thank you!

## 1. What is the difference between tangential and radial acceleration?

Tangential acceleration is the rate of change of an object's linear speed while radial acceleration is the rate of change of an object's direction of motion, also known as centripetal acceleration.

## 2. How do you calculate tangential and radial acceleration?

To calculate tangential acceleration, you can use the formula a = v^2/r, where a is the tangential acceleration, v is the linear speed, and r is the radius of the object's circular path. To calculate radial acceleration, use the formula a = v^2/r, where a is the radial acceleration, v is the linear speed, and r is the radius of the object's circular path.

## 3. What is an example of a tangential and radial acceleration problem?

An example of a tangential and radial acceleration problem could be a car driving around a circular track at a constant speed. The tangential acceleration would be the change in the car's linear speed as it moves along the track, while the radial acceleration would be the force keeping the car moving along the circular path.

## 4. How do tangential and radial acceleration affect an object's motion?

Tangential and radial acceleration work together to keep an object moving along a circular path. Tangential acceleration determines the object's linear speed, while radial acceleration determines the object's direction. Without these two types of acceleration, an object would not be able to maintain a circular motion.

## 5. What are some real-life applications of tangential and radial acceleration?

Tangential and radial acceleration are important in many real-life situations, including amusement park rides, car racing, and satellite orbits. They are also important in understanding the motion of planets and other celestial bodies in our solar system.

• Introductory Physics Homework Help
Replies
12
Views
727
• Introductory Physics Homework Help
Replies
7
Views
3K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
10
Views
415
• Introductory Physics Homework Help
Replies
9
Views
6K
• Introductory Physics Homework Help
Replies
4
Views
947
• Introductory Physics Homework Help
Replies
13
Views
1K
• Introductory Physics Homework Help
Replies
7
Views
6K
• Introductory Physics Homework Help
Replies
4
Views
3K
• Introductory Physics Homework Help
Replies
2
Views
927