Math Problem Statement
A car moving at a constant speed passed a timing device at t=0. After 6 seconds, the car has traveled 486 ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device.
Solution
The problem describes a car traveling at a constant speed, passing a timing device at , and then traveling 486 feet in 6 seconds. To model this situation as a linear function:
Step 1: Recall the structure of a linear equation.
The linear function takes the form: Where:
- : distance (in feet)
- : time (in seconds)
- : the rate of change (speed) in feet per second
- : the y-intercept (distance at ).
Step 2: Use the given information.
- At : The car is at the timing device, so .
- At : The car has traveled feet.
Step 3: Calculate the speed ().
Since the car travels a constant speed:
Step 4: Write the linear function.
Substituting and , the equation becomes:
Final Answer:
Would you like a deeper explanation or examples of applying this equation?
Related Questions:
- How can we interpret the slope in this context?
- What is the distance traveled after 10 seconds according to the function ?
- How would the function change if the car started 100 feet ahead of the timing device?
- If a second car travels at a constant speed of 90 ft/s, how long would it take for it to catch up to the first car?
- How would you model this if the car decelerates instead of traveling at a constant speed?
Tip:
Always identify the slope () as the "rate of change" to interpret real-world situations effectively in linear models.
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Rates of Change
Algebra
Formulas
d = mt + b
m = (change in distance) / (change in time)
Theorems
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Suitable Grade Level
Grades 7-9