Calculus-Based Physics by Jeffrey W. Schnick - HTML preview

Chapter 9 One-Dimensional Motion Graphs

(12) x vs. t just

600

becomes horizontal

here, like the top of

x

a hill. Must be

500

(11) Value of v is

horizontal here

[m]

decreasing meaning slope

since v = 0 at t = 20 s.

of x vs. t is decreasing meaning

it is “curved down”. Note that

400

values of v are still “+” so x is

increasing.

(8) Put point

here since 300

x = 225 m at

t = 0.

(10) v (below)

is increasing

(9) v is slope

200

meaning slope

of x vs. t, so, v

of x vs. t is

being constant

increasing

and “+” means

meaning

100

x vs. t is a

“curved up”

straight line

with “+” slope.

0 0

5

10

15

20

t [s]

35 m/s

v

35

(1) Put point

m

[ 30

s

]

here since

25

v = 15 m/s at

t = 0.

20

15 m/s

(3) Steady

15

increase in v

(2) Draw hori-

10

means straight

(4) Steady decrease

zontal line here

line from value

in v means straight

since v is con-

5

at 5

line from value at

s to value at

stant at 15 m/s.

10

10

s.

s to value at 20 s.

0 0

5

10

15

20

t [s]

4 m/s2

a

m

(6) a is slope of

[ ]

s2

v vs. t above;

v vs. t is straight

line with “+”

slope, so, a is

0

constant “+”

0

5 value meaning

10

15

20

t [s]

a vs. t is

(7) Above, v vs. t is a straight line with

(5) Constant v

horizontal.

“−“ slope, so, a is constant and “−“. When

means 0

a is constant, a vs. t is horizontal.

acceleration.

−3.5 m/s2

The key values on the v vs. t graph are givens so the only “mystery,” about the diagram above,

that remains is, “How were the key values on a vs. t obtained?” Here are the answers:

50