The height in feet of a free falling object t seconds after release is s(t)=-16t^2+ v_0t+s_0, where s_0 is the height(in feet) at which the object is realsed, and v_0 is the initial velocity (in feet per second). Suppose the coin is dropped from a height of 1454 feet.


D. At what time is the instanteous velocity equal to the average velocity if the coin found in part B?
Part B answer is -64ft/ sec
I do not know where to begin here please help

v = ds/dt

=-16(2)t
=-32 t

-32 t = -64 ??
if that is the question the answer is 2

Did you not look at my solution to the same question ?

http://www.jiskha.com/display.cgi?id=1468890453

All I can see wrong with it, I labeled part D as B

for B all you have to do it sub t = 1 and t = 3 into your velocity equation:
v = -32t.

To find the time at which the instantaneous velocity is equal to the average velocity, we need to first understand the concept of instantaneous velocity and average velocity.

Instantaneous velocity is the velocity of an object at a specific point in time, while average velocity is the total change in position of an object divided by the time interval. In this case, the instantaneous velocity is given by the derivative of the position function, and the average velocity is given by the change in position divided by the time interval.

Let's start by finding the instantaneous velocity. Given the position function s(t) = -16t^2 + v_0t + s_0 and the value of v_0 as -64 ft/sec, we can substitute the values into the position function:
s(t) = -16t^2 - 64t + s_0

Now, we need to find the derivative of the position function with respect to time (t). The derivative of -16t^2 is -32t, and the derivative of -64t is -64. Since the derivative of a constant (s_0) is 0, we can ignore it in this case. Therefore, the instantaneous velocity function is:
v(t) = -32t - 64

Next, we need to find the average velocity. In part B, it is given as -64 ft/sec. The average velocity is the total change in position (1454 - s_0) divided by the time interval (t). Since the time interval is not given, we will let it be represented as t.

The average velocity function is:
av(t) = (1454 - s_0) / t

Since the instantaneous velocity is equal to the average velocity, we can set the two functions equal to each other and solve for t:

-32t - 64 = (1454 - s_0) / t

Now, substitute the given value of s_0 as 1454 into the equation:

-32t - 64 = (1454 - 1454) / t

Simplifying further:

-32t - 64 = 0

Now, solve for t:

-32t = 64
t = -64 / -32
t = 2 seconds

Therefore, the instantaneous velocity is equal to the average velocity at t = 2 seconds.