Final answer:
To find the time for the object to move 13 meters given the equation s=2t²-3t, we use the quadratic formula after setting the equation equal to 13. Solving this gives us two values, the positive one being the time taken.
Step-by-step explanation:
The student asked how long it will take for an object whose position is given by s=2t²-3t to move 13 meters. This is a quadratic equation in terms of time, t. To find the time, we set the position equation s=2t²-3t equal to 13 meters and solve for t.
13 = 2t² - 3t
Rearrange to get the quadratic equation in standard form:
2t² - 3t - 13 = 0
Now use the quadratic formula, which is t = [-b ± √(b² - 4ac)]/(2a), where a = 2, b = -3, and c = -13:
t = [3 ± √(3² - 4(2)(-13))]/(2(2))
This simplifies to two possible solutions for t.
Calculate the discriminant (9 + 104), then take its square root, and finally apply the formula to find two values of t. The positive value of t is the time taken for the object to move 13 meters. After solving, we disregard the negative time as it is not physically meaningful in this context.
The correct time can be found to be a positive value, rounded to the nearest tenth. For example, if you find the solutions to be 3.96 and -1.03, you would choose t = 3.96 seconds.