Question 111607: The distance traveled by a ball roling down a ramp is given by the equation s(t)=5tsquared, where t is the time after the ball is released, in seconds, and s(t) is mearsured n feet. What is the average speed of the ball for the time t=3 through t=4.5? Express your answer as a decimal to the nearest tenth.
I came up with s=15 for the 3 second time and s=22.5 for the 4.5 time. I plugged in the number to get 45 seconds and 101.25 seconds and averaged the two. I got an average of 73.125 or 73.1 feet per second. Does that look right?
I don't have the ISBN number for the Math Counts book; the teacher does.
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website! The distance traveled by a ball roling down a ramp is given by the equation
s(t)=5tsquared, where t is the time after the ball is released, in seconds,
and s(t) is mearsured n feet. What is the average speed of the ball for the
time t=3 through t=4.5? Express your answer as a decimal to the nearest tenth.
I came up with s=15 for the 3 second time and s=22.5 for the 4.5 time. I
plugged in the number to get 45 seconds and 101.25 seconds and averaged the
two. I got an average of 73.125 or 73.1 feet per second. Does that look right?
No, sorry. You averaged the two distances.
That is incorrect.
You must use the formula for average speed.
Total distance
Average speed = ————————————————
Total time
Notice that in finding the average speed,
you do not average anything. [That sounds
like an oxymoron, doesn't it?]
To find the total distance we find
1. the distance it had traveled in exactly
4.5 seconds, which you correctly found
to be 101.25 feet.
and
2. the distance it had traveled in exactly
3 seconds, which you also found correctly
as 45 feet.
Then to find the distance it traveled between
the instant when 3 seconds had passed and the
instant when 4.5 seconds had passed, we subtract
the second distance from the first distance,
getting
101.25 feet - 45 feet or 56.25 feet which it
traveled between 3 and 4.5 seconds.
So the Total distance = 56.25 feet
Now to find the Total time. That is simply 4.5
seconds minus 3 seconds or 1.5 seconds
So the total time = 1.5 seconds.
Substituting in
Total distance
Average speed = ————————————————
Total time
we get
56.25 feet
Average speed = ————————————— = 37.5 ft/sec
1.5 seconds
Edwin
|
|
|
