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calculusxy
 one year ago
1. How far will an object move in one second if its average speed is 5 m/s?
A. 5 meters
2. How far will a freely falling object have fallen from a position of rest when its instantaneous speed is 10 m/s?
A. 75 meters
3. An object dropped from rest and falls freely. After 6 seconds, calculate its instantaneous speed, average speed, and distance fallen.
A. Instantaneous speed: 58.8 m/s
Average Speed : 53.9 m/s
Distance : 313.6 meters
4. If a freely falling rock were equipped with an odometer, would the readings for the distance fallen each second stay the same...
calculusxy
 one year ago
1. How far will an object move in one second if its average speed is 5 m/s? A. 5 meters 2. How far will a freely falling object have fallen from a position of rest when its instantaneous speed is 10 m/s? A. 75 meters 3. An object dropped from rest and falls freely. After 6 seconds, calculate its instantaneous speed, average speed, and distance fallen. A. Instantaneous speed: 58.8 m/s Average Speed : 53.9 m/s Distance : 313.6 meters 4. If a freely falling rock were equipped with an odometer, would the readings for the distance fallen each second stay the same...

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calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1...increase with tie, or decrease with time? A. The instantaneous speed would increase so the distance would increase as well.

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1Can you make sure the answers?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2A. Is correct because $$ 5 \frac{m}{\cancel{s}}\times 1~\cancel{s}=5~m $$ Notice how the seconds cancel each other out and you are left with just meters ,\(m\)?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2For 2 you need to use the following equation $$ v^2 = u^2 + 2as $$ where u is the initial velocity, a is the acceleration of gravity, s is the distance traveled and v is the final velocity: https://en.wikipedia.org/wiki/Equations_of_motion#Kinematic_equations_for_one_particle So $$ 10^2=0^2+2s\times 9.81\\ \implies s=\frac{100}{2\times 9.81}=5~m $$ Does this make sense?

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1Answer would be 5M?

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1how would it be 5m if it is travelling 10m/s

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2dw:1436316669347:dw (ignore the t=1/2 seconds above) It takes $$ v/a=10/9.81=1.01\text{ second} $$ to go from 0 to 10 m/s In that time period, it is accelerating. If it were going a constant speed of 10 m/s then is 1 second it would have traveled 10 m, but it didn't START at 10 m/s, it started at 0 m/s. Right?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2For # 3 Instantaneous speed: $$ v=at\\ v=9.8\times 6=58.8~m/s $$ Average speed: $$ \frac{1}{6}\int_0^6 at~dt=\frac{1}{6}a\frac{t^2}{2}_0^6=\frac{9.8\times 6^2}{12}=29.4~m/s $$ distance $$ s=\frac{1}{2}at^2=\frac{1}{2}9.8(6)^2=176.4~m $$ Does this make sense?

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1Sorry but I am just a rising eighth grader so i don't understand the average speed part.

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2How did you determine average?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2You can graph it, that's another way, want to try that?

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1what i did was: 5 sec = 49 m/s 6 sec = 58.8 m/s 49 + 58.8 / 2 = 53.9

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2Why did you use 5 seconds here?

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1well that's what my teacher said for me to use

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.12 seconds => average speed 19.6 + 9.8 /2 = 14.7 m/s

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.19.8 (1st second) 19.6 (2nd second)

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2Yes, that is a good approach, keep going

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1so 53.9 is correct?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2It will be an estimate... but if you want a formula, use: $$ \frac{v_{final}v_{initial}}{2}=\frac{v_{final}0}{2}=\frac{a t}{2} $$ Because the initial velocity is 0 and final velocity = \(at\).

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2Average speed should be 9.8*6/2. a is the acceleration of gravity = 9.8 m/s^2

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2So did you get the distance traveled?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2Ok for the final one...

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2An odometers measures distance traveled, right?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2And acceleration is change in velocity per unit time, so your speed is changing every second, in fact its increasing every second, right?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2Ok, so velocity is changing. If in one second you are going 1 m/s and in the next second you are going 2 m/s then the distance you are traveling every second is increasing. So the odometer will show for the 1st second one meter and the odometer will show for the second second, 2 meters. Do you see that?

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.1yes so it's increasing right?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2yes, because velocity is increasing. If you were slowing down, then the odometer would do the opposite
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