For three seconds, a particle moves along a straight path with velocity function given by v(t)...

  

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For three seconds, a particle moves along a straight path with velocity function given by v(t) = 6t 18t+12, where velocity is measured in feet per second. a. Sketch a graph of the velocity function for the first three seconds and label each axis with a number scale and measurement units. Include the graph when you turn in your work. b. Over what interval(s) of time is the particle moving forward? How do you know? c. Over what interval(s) of time is the particle moving backward? How do you know? d. When is the particle stopped? How do you know? e. Integrate the velocity function from 0.5 seconds to 2 seconds. Show your work. Explain what your answer means for the particle. f. Find the total distance traveled by the particle in the first three seconds, so from 0 seconds to 3 seconds. Show your work. For three seconds, a particle moves along a straight path with velocity function given by v(t) = 6t 18t+12, where velocity is measured in feet per second. a. Sketch a graph of the velocity function for the first three seconds and label each axis with a number scale and measurement units. Include the graph when you turn in your work. b. Over what interval(s) of time is the particle moving forward? How do you know? c. Over what interval(s) of time is the particle moving backward? How do you know? d. When is the particle stopped? How do you know? e. Integrate the velocity function from 0.5 seconds to 2 seconds. Show your work. Explain what your answer means for the particle. f. Find the total distance traveled by the particle in the first three seconds, so from 0 seconds to 3 seconds. Show your work.