Math Problem Statement
If a rock is thrown upward on the planet Mars with a velocity 6 m/s, its height in meters t seconds later is given by y = 6t − 1.86t^2. (Round your answers to two decimal places.) (a) Find the average velocity (in m/s) over the given time intervals.
[1,1.1]____m/s
Solution
To calculate the average velocity of the rock over the time interval , we use the formula for average velocity:
where:
- is the height function ,
- and .
Step 1: Calculate
Substitute into the height function:
Step 2: Calculate
Substitute into the height function: First, calculate each term:
Step 3: Calculate the average velocity
Now, use the average velocity formula:
Answer:
The average velocity over the interval is approximately 2.09 m/s.
Would you like further clarification, or do you have more questions?
Here are 5 related questions you might find interesting:
- What is the average velocity over the interval ?
- How can we find the instantaneous velocity at ?
- What is the maximum height the rock will reach?
- How long does it take for the rock to hit the ground?
- What is the initial acceleration of the rock?
Tip: Average velocity over a small interval can be a good approximation of instantaneous velocity at a point.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Average Velocity
Formulas
Average velocity = (y(t2) - y(t1)) / (t2 - t1)
Height function: y = 6t - 1.86t^2
Theorems
Average Velocity Theorem
Suitable Grade Level
Grades 9-12
Related Recommendation
Calculate Average and Instantaneous Velocity of a Rock on Mars
Average Velocity of a Rock Thrown on Mars Using Quadratic Functions
Calculate Average and Instantaneous Velocity of a Rock Thrown Upward on Mars
Calculate Average Velocity of a Rock on Mars: Physics Problem
Calculating Average Velocity in Kinematics Problems: Mars Example