SOLUTION: The height of a falling object dropped form a height of 100m is described by h=100-16t2 where t is time measured in seconds. Find i) The velocity at t = 2 ii) The accelerati

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Question 364182: The height of a falling object dropped form a height of 100m is described by h=100-16t2 where t is time measured in seconds.
Find i) The velocity at t = 2
ii) The acceleration at t = 2

Found 2 solutions by Earlsdon, Alan3354:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The height (as a function of time, t) of an object falling from 100 meters is described by:
h%28t%29+=+100-16t%5E2
i) Find the velocity at t = 2
The velocity is the rate of change of distance with respect to time, t.
If we take the first derivative of the height fuction, we will get the eqation for the velocity.
dh%2Fdt+=+-32t and at t=2, we get:
dh%2Fdt+=+-32%282%29 dh%2Fdt+=+v
v+=+-64meters/second. The negative indicates a downward direction.
ii) Find the acceleration at t = 2.
Acceleration, which is the rate of change of velocity with respect to time, t, can be found by taking the second derivative of the height function (h%28t%29+=+100-16t%5E2):
d%5E2t%2Fdt%5E2+=+d%28dh%2Fdt%29%2Fdt=d%28-32t%29%2Fdt+=+-32meters/second squared.
d%5E2t%2Fdt%5E2+=+a
a+=+-32meters/second squared. A constant.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
This problem has the height in meters, but uses the formula for feet.