Math Problem Statement

A car travels northward on a straight stretch of highway. The graph below shows the velocity of the car during a 20-second time interval. What is the acceleration of the car during the interval AB?

Solution

To find the acceleration of the car during the interval AB on the velocity-time graph, we need to calculate the rate of change of velocity over that interval. This can be done using the slope formula:

Acceleration=ΔvelocityΔtime\text{Acceleration} = \frac{\Delta \text{velocity}}{\Delta \text{time}}

From the graph:

  • Point A corresponds to t=0t = 0 seconds and v=0v = 0 m/s.
  • Point B corresponds to t=4t = 4 seconds and v=20v = 20 m/s.

Using the slope formula, we calculate the acceleration as follows: Acceleration=20m/s0m/s4s0s=20m/s4s=5m/s2\text{Acceleration} = \frac{20 \, \text{m/s} - 0 \, \text{m/s}}{4 \, \text{s} - 0 \, \text{s}} = \frac{20 \, \text{m/s}}{4 \, \text{s}} = 5 \, \text{m/s}^2

This means the acceleration of the car during the interval AB is 5m/s25 \, \text{m/s}^2, which isn't one of the options provided. If this value seems unexpected based on the options, please double-check that the points A and B are correctly identified or consider if there's a scale factor on the graph that wasn't accounted for.

Would you like more details on this calculation or have any other questions? Here are some topics we could explore further:

  1. How to determine velocity from a velocity-time graph.
  2. How to calculate the total distance traveled using a velocity-time graph.
  3. The relationship between acceleration, velocity, and displacement.
  4. Explanation of uniform acceleration.
  5. Understanding the area under a velocity-time graph.

Tip: When working with graphs, always check if the axes are scaled uniformly or if any scaling factors are applied.

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Math Problem Analysis

Mathematical Concepts

Physics
Kinematics
Velocity-Time Graph

Formulas

Acceleration = Δvelocity / Δtime

Theorems

Newton's Second Law of Motion

Suitable Grade Level

Grades 9-12