7.1.1 Acceleration and the Derivative

Question 1

Acceleration and the Derivative

Answer 1

• Velocity is the rate of change of position. Acceleration is the rate of change of velocity.
• Tangent lines can be used to approximate functions that are difficult to evaluate. The slopes of tangent lines can be used to optimize outputs such as profits and
  areas.

Question 2

note

Answer 2

• Velocity is the rate of change of position.
• Acceleration is the rate of change of velocity. So
  the velocity function is the derivative of the position
  function and the acceleration function is the
  derivative of the velocity function.
• The connection between instantaneous rate, the
  derivative, and the slope of the tangent line give rise
  to many different applications of differential calculus.
  Tangent lines can be used to approximate the
  values of hard-to-evaluate functions as well as the
  roots of functions.
• The derivative can also be used to optimize
  function outputs. The behavior of tangent lines can
  tell you where functions attain maximum and
  minimum values.

Question 3

Suppose an object falling out of an airplane has a velocity of v (t) = −32t + 64 where t is in seconds and v is in feet per second. What is the acceleration of the object when t = 1?

Answer 3

−32 ft/sec2

Question 4

Given that a particular moving object’s velocity is given by the equation v(t)=−32t+110, what is the equation for the object’s acceleration?

Answer 4

a (t) = −32

Question 5

Given that a particular moving object’s velocity is given by the equation v(t)=65t−2t^2, what is the equation for the object’s acceleration?

Answer 5

a (t) = 65 − 4t`

Question 6

Given that a particular moving object’s velocity is given by the equation v(t)=65−3t, what is the equation for the object’s acceleration?

Answer 6

a (t) = −3

Question 7

Which of the following statements about acceleration is true?

Answer 7

Acceleration is the rate of change in velocity.

Question 8

A car is moving at a constant acceleration of 3 m / sec2. If the car is moving with a velocity of 20 m / sec at t = 0, how fast is the car moving when t = 3?

Answer 8

29 m / sec

Question 9

A jogger is moving at a constant velocity of 8 ft / sec. How far has the jogger moved after 20 seconds?

Answer 9

160 feet