1.1.1 - Acceleration and the Derivative

Question 1

Which of the following statements about acceleration is true?

Answer 1

Acceleration is the rate of change in velocity.

Question 2

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 2

a(t) = -3

Question 3

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 3

a(t) = 65 - 4t

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)=-32t^2+110, what is the equation for the object’s acceleration?

Answer 5

a(t) = -64

Question 6

Given that a particular moving object’s velocity is given by the equation v(t)=45t-55, what is the equation for the object’s acceleration?

Answer 6

a(t) = 0

Question 7

A car is moving at a constant acceleration of 3 m/sec^2. 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 7

29 m/sec

Question 8

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

Answer 8

160 feet

Question 9

Suppose f(x) is a continuous differentiable function and you are given that f’‘(x) is always positive. Which of the following statements must be true?

Answer 9

f’(x) is always increasing

Question 10

Suppose that the position of an object on a number line is given by p(t) = t^2 - 3t + 1 where t is in seconds and p is in centimeters. What is the acceleration of the object when t = 2 seconds?

Answer 10

2 cm/sec^2

Question 11

Suppose the position of a particle on a number line is given by p(t) = 3t^3 - 3t, where t is in minutes and p is in meters. Which of the following equations represents the acceleration of the object?

Answer 11

a(t) = 18t

Question 12

Suppose an object is 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 12

-32 ft/sec^2