Solve Elevator Force: 100kg, X, 10s, a*

[HumorMe81]

100 kg elevator acclerates up at rate avg a*. What's the avg force acting on the elevator if it covers a distance X over a period of 10s?

a* denotes average acceleration
a. 2X + 1000
b. 100(a* + 1)
c. 2a* + 1000
d. 2a*X

I set up a free body diagram to show all the forces acting on the elevator. There's a downward force due to gravity, Fg, the net upward force, Fn, causing the acceleration.

Fn - Fg = ma*
Fn = ma* + Fg

The question states that it travels a distance of X over 10 sec

a* = delta V/delta t
delta V = X/t , which the question gives me
delta V = x/10s, i substituted this into the a* equation and got
a* = x/100s

when i plug this into my net force equation:

Fn = ma* + Fg
Fn = m(a* + g)
Fn = 100kg(x/100s + 10m/s^2)
Fn = X + 1000

I can't seem to figure out why my answer doesn't match any of the answer choices. Can someone please point out what I'm doing wrong?
Thanks

 

[flatmaster]

You used the wrong kinetic equation. You calculated your final velocity incorrectly.

 

[HumorMe81]

You used the wrong kinetic equation. You calculated your final velocity incorrectly.

avg velocity comes to mind since the question says the elevator travels a distance x over a period of 10s. If i solve the problem using this information, the answer comes out to be 2X + 1000.
But avg acceleration is equal to delta v/ delta t, not avg velocity. And also, using avg velocity would mean i have constant acceleration and i don't.

I really think this is a ridiculous question, very loosely termed.

 

[Doc Al]

a* = delta V/delta t

OK.

delta V = X/t , which the question gives me

No, X/t gives the average speed, not the change in speed.

 

[HumorMe81]

ok, so does that mean avg speed is = 2X/t?
if so, then the answer is a. 2X + 1000

I still don't see the relationship between avg speed and avg acceleration.

 

[HallsofIvy]

ok, so does that mean avg speed is = 2X/t?
if so, then the answer is a. 2X + 1000

I still don't see the relationship between avg speed and avg acceleration.

There isn't any. And average speed is irrelevant. Force= mass * acceleration, not mass* speed. If the speed were constant over the trip, there would be no force.

 

[HumorMe81]

There isn't any. And average speed is irrelevant. Force= mass * acceleration, not mass* speed. If the speed were constant over the trip, there would be no force.

ok, if the acceleration were constant and the initial velocity were given to be 0, then i see some sense in solving this problem. And even then the answer wouldn't match any of the given answers.