Math Problem Statement
A car enters the freeway with a speed of 6.4 m/s and accelerates uniformly for 3.2 km in 3.5 min. How fast is the car moving after this time?
Solution
To solve this problem, we need to calculate the final speed of the car after it has accelerated uniformly. We'll use the following kinematic equation for uniform acceleration:
Where:
- is the final velocity (what we are solving for).
- is the initial velocity (6.4 m/s).
- is the acceleration (to be determined).
- is the time (converted to seconds).
Step 1: Convert distance and time into consistent units.
- Distance traveled,
- Time,
Step 2: Find acceleration using the second kinematic equation:
Substitute the known values:
Now, we can solve for and then use it to find the final velocity . Let's compute this.The final speed of the car after accelerating for 3.5 minutes is approximately .
Would you like more details on the solution, or do you have any questions?
Here are some related questions to expand your understanding:
- How does uniform acceleration affect the distance traveled over time?
- What would happen if the initial speed was different, say 10 m/s, for the same time and distance?
- How can you calculate the average speed during the acceleration?
- What would the acceleration be if the time was doubled but the distance stayed the same?
- How can you determine the total distance traveled with non-uniform acceleration?
Tip: Always ensure units are consistent (e.g., converting time to seconds) when solving physics problems!
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Math Problem Analysis
Mathematical Concepts
Kinematics
Uniform Acceleration
Conversion of Units
Formulas
v_f = v_i + a t
d = v_i t + (1/2) a t^2
Theorems
Uniform acceleration equations in kinematics
Suitable Grade Level
Grades 9-12
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