Final answer:
To find the distance traveled during a given time interval, you need to integrate the expression for velocity with respect to time. Given the expression t² + 2t - 15, integrate it to find the equation for displacement and evaluate the displacement equation at the boundaries of the time interval to find the distance traveled.
Step-by-step explanation:
To find the distance traveled during a given time interval, we need to integrate the expression for velocity with respect to time.
Given the expression t² + 2t - 15, we can integrate it to find the equation for displacement: ∫(t² + 2t - 15) dt = (1/3)t³ + t² - 15t + C.
To find the distance traveled during the given time interval, we need to evaluate the displacement equation at the boundaries of the time interval and calculate the difference: (1/3)(t₂³ - t₁³) + (t₂² - t₁²) - 15(t₂ - t₁).
Considering the given time interval, we have t₁ = 5 s and t₂ = 10 s. Substituting these values into the equation, we get (1/3)(10³ - 5³) + (10² - 5²) - 15(10 - 5) = 315 m.