If velocity v(t) = 4t, distance traveled from t=0 to t=3 is?

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Multiple Choice

If velocity v(t) = 4t, distance traveled from t=0 to t=3 is?

Explanation:
Distance traveled is found by adding up how far the object moves over the time interval, which means integrating velocity with respect to time. For v(t) = 4t from t = 0 to t = 3, compute the integral ∫ from 0 to 3 of 4t dt. The antiderivative is 2t^2, so evaluate: 2(3)^2 − 2(0)^2 = 18. Because the velocity is positive on this interval, the distance traveled equals this displacement. So the distance is 18 units.

Distance traveled is found by adding up how far the object moves over the time interval, which means integrating velocity with respect to time. For v(t) = 4t from t = 0 to t = 3, compute the integral ∫ from 0 to 3 of 4t dt. The antiderivative is 2t^2, so evaluate: 2(3)^2 − 2(0)^2 = 18. Because the velocity is positive on this interval, the distance traveled equals this displacement. So the distance is 18 units.

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