Position Velocity and Acceleration example 1

The video tutorial explains a problem involving an Olympic runner's position, velocity, and acceleration during a 100-meter race. The velocity is given as a function of time, and the task is to find the runner's position and acceleration at any time. The tutorial covers differentiating velocity to find acceleration and integrating velocity to find position, using initial conditions to solve for constants. Graphs of position, velocity, and acceleration are analyzed to understand the runner's motion.

What is the given velocity equation for the Olympic runner?

• v = 2/7 t^2 - 4t

• v = -2/7 t^2 - 4t

• v = -2/7 t^2 + 4t

• v = 2/7 t^2 + 4t

How is acceleration related to velocity in this problem?

• Acceleration is the integral of velocity.

• Acceleration is the derivative of velocity.

• Acceleration is the square of velocity.

• Acceleration is the inverse of velocity.

What is the acceleration equation derived from the velocity equation?

• a = -4/7 t + 4

• a = 4/7 t - 4

• a = -4/7 t - 4

• a = 4/7 t + 4

What mathematical process is used to find the position from velocity?

• Differentiation

• Multiplication

• Subtraction

• Integration

What is the integration constant when deriving the position equation?

• 1

• 0

• 2

• 4

How does the position graph behave over time according to the video?

• It decreases linearly.

• It remains constant.

• It increases gradually.

• It fluctuates randomly.

What happens to the runner's acceleration towards the end of the race?

• It becomes zero.

• It becomes positive.

• It becomes negative.

• It remains constant.