Free Printable Calculus Motion Basics

Worksheets

Calculus Motion Basics

Total questions: 26

Worksheet time: 49mins

Name

Class

Date

Position and velocity are graphed here. Which is which?

blue is position, red is velocity

red is position, blue is velocity

There is not enough information to determine

As derivative of position, red is velocity, cm/sec, of a particle moving on a horizontal line. What is the particle doing from 0 to 2 seconds? Do not choose the graph. It's showing speed and FYI.

slowing down, moving forward (right)

slowing down, moving backward (left)

speeding up, moving backward

speeding up, moving forward

These are graphs for the motion of a particle on a horizontal line. Which of these is the best description of their relationship?

velocity is the absolute value of speed

speed is the absolute value of velocity

velocity is stronger than speed

speed wants nothing to do with velocity

These are graphs for the motion of a particle on a horizontal line. On what intervals is the particle speeding up? (Speed is increasing) Check all that apply.

(0,1)

(1,2)

(2,3)

(3,4)

(4,6)

To find average velocity over a time interval, divide the change in ___________by the change in time.

position

speed

velocity

acceleration

s(t) = t² - 20
Find the average velocity from t = 3 to t = 5.

Given the graph of the position function, which graph below shows the velocity of the function?

If the position of a particle is represented by s(t) = -t² + 1, what is its instantaneous velocity at t = 1?

Velocity = 0

Velocity = 1

Velocity = -1

Velocity = -2

Acceleration is the rate of change of ________________.

position

velocity

speed

swag

10.

Using s(t) as position and a(t) as acceleration, this integral is equal to

s(5) - s(1)

a(5) - a(1)

the distance traveled

all of these

11.

Using s(t) as position and a(t) as acceleration, this integral is equal to s(5) – s(1). This represents ___________________. Check all that apply.

change of position

displacement

position at 5 minus position at 1

distance traveled over a 4 second period

microwave settings

12.

A turtle starts at x = 2 and travels to the right to stand briefly at x = 5, and then travels to the left and comes to a stop at x = -1. What is the turtle's total distance traveled?

negative 3 spaces

5 spaces

7 spaces

9 spaces

13.

A turtle starts at x = 2 and travels to the right to stand briefly at x = 5, and then travels to the left and comes to a stop at x = -1. What is the turtle's change in position (displacement)?

negative 3 spaces

positive 3 spaces

7 spaces

6 spaces

14.

Which of these represents velocity of this position function?

sqrt( 3(x²) + 1)

sqrt( (3x)² + 1)

(2x)sqrt( 3(x²) + 1)

none of these

15.

Speed

v(t) > 0

a(t) > 0

∣v(t)∣

∣a(t)∣

16.

Given this velocity graph, speed is

Increasing, Positive

Increasing, Negative

Decreasing, Positive

Decreasing, Negative

17.

Given this velocity graph, the acceleration of the particle is

Positive, Increasing

Positive, Decreasing

Negative, Increasing

Negative, Decreasing

18.

An object is speeding up when

v(t) > 0

a(t) > 0

v(t) and a(t) are the same sign

v(t) and a(t) are different signs

19.

Average Rate of Change

Average Value of f

Intermediate Value Theorem

Rolle's Theorem

20.

This graph is velocity of a particle moving on a horizontal number line with initial position at -5, s(0) = -5. What is the particle doing from 0 to 2 seconds?

moving down

moving right

moving left

moving out

21.

This graph is velocity, cm/sec, of a particle moving on a horizontal number line with initial position at -5, s(0) = -5. From 0 to 2, the particle moves backward. From 2 to 4, the particle moves forward. After 4 seconds, is the particle to the left or right of -5 on the number line?

left a smidge

right a smidge

There is not enough information to determine

why is this particle the object of our quandary?

22.

Red is velocity, cm/sec, green is speed. Particle motion on horizontal line. What is the total distance traveled from 0 to 2 seconds?

8 cm

4 cm

4 cm²

cannot be determined

23.

Displacement of a particle is different than distance traveled.

always true

sometimes true

never true

only on Tuesdays

24.

Adding up area between the red curve and the x-axis gives

displacement

distance traveled

position at 6

nothing special

25.

Using s(t) as position and v(t) as velocity, distance traveled would be

$\int_0^6s\left(t\right)\ dt$

$\int_0^6v\left(t\right)dt$

$\int_0^6\left|s\left(t\right)\right|dt$

$\int_0^6\left|v\left(t\right)\right|dt$

26.

Which of these is integrating speed?