Instantaneous Speed Application Problem

In summary, the conversation involves a task given by a teacher to create a function for the instantaneous speed of a laser point revolving around a rectangular room. The group has found the dimensions of the room and the RPM of the laser, which has been converted to radians per second. They are now discussing how to define variables, such as "x", to represent the relevant quantities in the problem.
  • #1
jjayla12
2
0

Homework Statement



My teacher put us into groups and we each selected a wall of the rectangular room. He attached some sort of machine to the wall that spins in a circle with a laser on it, creating a laser point revolving around the walls. Our task is to create a function for the instantaneous speed of the laser point at any point x on our wall.

2. The attempt at a solution
1. We found the dimensions of the room. The red dot indicates where the laser is at. We have the left wall.
calc.png

2. We found the RPM by counting how many times the laser hit one spot on the wall over a interval of 1 minute.
RPM = 36
3. Converted to radians per second 6pi/5

Now we don't know what to do from here.
 
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  • #2
How about defining some variables to represent the relevant quantities in your problem? For instance, you referred to "x". What is x?
 
  • #3
X would be any distance on our wall from 0 to 26.75.
 
  • #4
Measured from where? You need to precisely define the quantities here. We can't read your mind. Are there any other variables?
 

FAQ: Instantaneous Speed Application Problem

What is an instantaneous speed application problem?

An instantaneous speed application problem involves using the concept of instantaneous speed to solve real-world problems. It requires applying the formula for instantaneous speed, which is the limit of average speed as the time interval approaches zero.

What is the formula for instantaneous speed?

The formula for instantaneous speed is v = lim Δt→0 Δx/Δt, where v is the instantaneous speed, Δx is the change in position, and Δt is the change in time.

How is instantaneous speed different from average speed?

Instantaneous speed is the speed at a specific moment in time, while average speed is the total distance traveled divided by the total time taken. Average speed takes into account the entire journey, while instantaneous speed focuses on a specific point in time.

What are some examples of instantaneous speed application problems?

Examples of instantaneous speed application problems include finding the speed of a car at a given moment, determining the velocity of a falling object at a specific time, or calculating the acceleration of a runner at the starting line of a race.

Why is it important to understand instantaneous speed?

Understanding instantaneous speed is important because it allows us to accurately describe the motion of objects at any given moment. It is also a fundamental concept in physics and is essential for solving many real-world problems involving motion.

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