2015 AP Calculus AB/BC 3cd | AP Calculus AB solved exams | AP Calculus AB | Khan Academy

TL;DR

Bob's velocity and acceleration are calculated using a velocity function. The average velocity over a given interval is also determined.

Transcript

• [Voiceover] Bob is riding his bicycle along the same path. For zero is less than or equal to t is less than or equal to 10. Bob's velocity is modeled by B of t is equal to t to the third minus six t squared plus 300, where t is measured in minutes and B of t is measured in meters per minute. Find Bob's acceleration at time t equals five. Well acc... Read More

Key Insights

• 🥡 Bob's acceleration is found by taking the derivative of his velocity function, B(t).
• 🤒 The unit for acceleration is meters per minute squared.
• ⌛ Average velocity is calculated by finding the area under the velocity curve divided by the change in time.

Questions & Answers

Q: How can Bob's acceleration be calculated?

Bob's acceleration is the derivative of his velocity function with respect to time. By taking the derivative of B(t) = t^3 - 6t^2 + 300, we can find B'(t) which represents his acceleration.

Q: What is the unit of Bob's acceleration?

Bob's velocity is measured in meters per minute, so his acceleration will also be measured in the same unit, which is meters per minute squared.

Q: How is average velocity calculated?

Average velocity is determined by finding the area under the velocity curve from t = 0 to t = 10, and then dividing it by the change in time. It can be calculated using the formula: (1/10) ∫[0 to 10] B(t) dt, where B(t) = t^3 - 6t^2 + 300.

Q: What is the average velocity of Bob during the interval from t = 0 to t = 10?

The average velocity of Bob during this interval is 350 meters per minute. This is calculated by finding the definite integral of B(t) = t^3 - 6t^2 + 300 from t = 0 to t = 10 and dividing the result by 10.

Summary & Key Takeaways

• Bob's velocity is modeled by the function B(t) = t^3 - 6t^2 + 300, where t is measured in minutes and B(t) is measured in meters per minute.

• Bob's acceleration at time t = 5 is found by evaluating the derivative of the velocity function, B'(t), at t = 5.

• The average velocity of Bob during the interval from t = 0 to t = 10 is calculated by finding the area under the velocity curve and dividing it by the change in time.