Math Problem Statement

The position x of an object as a function of time t. What are the avaregae speed and average velocity for the first 4 seconds? Pick the answer you think is correct below

7.5 m/s; 32.5 m/s

2.5 ms/; (-2.5 m/s)

32.5 m/s; (-7.5 m/s)

32.5 m/s; 32.5 m/s

(-2.5 m/s); 2.5 m/s

(-7.5 m/s); 32.5 m/s

I don't know

Solution

To determine the average speed and average velocity over the first 4 seconds, we need more information regarding the object's motion. Typically, the position function x(t)x(t) would be given in terms of time tt, such as a polynomial or other expression, so we can compute:

  1. Average speed: This is calculated as the total distance traveled divided by the total time.
  2. Average velocity: This is calculated as the displacement (change in position) divided by the total time.

If you're trying to solve a problem based on this list of answers, we would need the exact form of x(t)x(t) to calculate these values.

However, from the given options, let's consider them:

  • The answers seem to provide both average speed and average velocity, and the key differences are whether the quantities are positive or negative.
  • Average speed should always be positive, as it represents the total distance covered.
  • Average velocity can be negative, indicating the direction of the displacement.

If you have the position function x(t)x(t), I can help compute the exact values. If not, I would recommend choosing "I don't know" since we can't calculate the values without more information.

Would you like to provide more information, or pick the option you think is best?


Here are 5 related questions to deepen your understanding:

  1. What is the difference between distance and displacement?
  2. How do you find average velocity when given a position-time graph?
  3. Why is average speed always positive, but average velocity can be negative?
  4. Can an object have zero velocity but non-zero speed at the same time?
  5. How does acceleration affect both speed and velocity over time?

Tip: To calculate average velocity, always focus on the net displacement, not the total path distance!

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Math Problem Analysis

Mathematical Concepts

Kinematics
Average Speed
Average Velocity

Formulas

Average speed = total distance / total time
Average velocity = displacement / total time

Theorems

Kinematic Equations

Suitable Grade Level

Grades 9-12