The table below shows the distance d(t) in meters that an object travels in t seconds:

t

(seconds)

d(t)

(meters)

1

15

2

60

3

135

4

240

What is the average rate of change of d(t) between 2 seconds and 4 seconds, and what does it represent?

50 m/s; it represents the average speed of the object between 2 seconds and 4 seconds

90 m/s; it represents the average speed of the object between 2 seconds and 4 seconds

90 m/s; it represents the average distance traveled by the object between 2 seconds and 4 seconds

50 m/s; it represents the average distance traveled by the object between 2 seconds and 6 seconds

The best answer to the physics question above would be the second statement. The average rate of change between 2 seconds and 4 seconds would be 50m/s and it represents the average speed of the object. The other choices do not point to the correct answer.

Answer Link

OrethaWilkison OrethaWilkison · Answer 2 · 2019-03-04T05:50:30-05:00

Answer:

Option B is correct

90 m/s; it represents the average speed of the object between 2 seconds and 4 seconds

Step-by-step explanation:

Average rate of change(A(x)) for f(x) over interval [a,b] is given by:

\(A(x) = \frac{f(b)-f(a)}{b-a}\)

As per the statement:

here, d(t) is the distance in meter and t is the time in seconds.

For t = 2 seconds

then;

d(2) = 60 meters

and

for t =4 seconds

then;

d(4) = 240 meters

Then by definition of average rate we have;

\(A(x) = \frac{d(4)-d(2)}{4-2}\)

⇒\(A(x) = \frac{240-60}{2}\)

⇒\(A(x) = \frac{180}{2} = 90\) m/s

Therefore, the the average rate of change of d(t) between 2 seconds and 4 seconds is, 90 m/s

It represents the average speed