The total distance d, in meters, traveled by an object moving in a straight line can be modeled by a quadratic function that is defined in terms of t, where t is the time in seconds. At a time of 10.0 seconds, the total distance traveled by the object is 50.0 meters, and at a time of 20.0 seconds, the total distance traveled by the object is 200.0 meters. If the object was at a distance of 0 meters when , then what is the total distance traveled, in meters, by the object after 30.0 seconds?
Correct answer: 450
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Explanation
The correct answer is 450. The quadratic equation that models this situation can be written in the form , where a, b, and c are constants. It’s given that the distance, d, the object traveled was 0 meters when seconds. These values can be substituted into the equation to solve for a, b, and c: . Therefore, , and it follows that . Since it’s also given that d is 50 when t is 10 and d is 200 when t is 20, these values for d and t can be substituted to create a system of two linear equations: and , or and . Subtracting the first equation from the second equation yields , or . Substituting for a in the first equation and solving for b yields . Therefore, the equation that represents this situation is . Evaluating this function when seconds yields , or meters.
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id cb_question_bank:caa574d3-4857-4ebe-843e-8bd1a803b148 · question 4b642eef · IBN 026162-DC
· JSON