Asilver dollar is dropped from the top of a building that is 1344 feet tall. use the position function below for free-falling objects. s(t) = -16t^(2) + v0t + s0

(a) determine the position and velocity functions for the coin. s(t)= v(t)=

(b) determine the average velocity on the interval [3,4]. = ft/s

(c) find the instantaneous velocities when t = 3 s and t = 4 s. v(3)= v(4)=

(d) find the time required for the coin to reach the ground level. t=

(e) find the velocity of the coin at impact. vf =/s

a. position function of the coin:

    Now the velocity function:

b.

c.        &  

d.

e.

Explanation:

Given:

Given position function associated with free falling objects:

here:

initial height

initial velocity

time of observation

a)

position function of the coin:

∵the object is dropped it was initially at rest

Now the velocity function:

b)

we know average velocity is given as:

Displacement in the given interval:

Now,

c)

Instantaneous velocity at t = 3 s:

Instantaneous velocity at t = 4 s:

d)

At ground we  have s=0:

Put this in position function:

e)

Velocity of the coin at impact:

explanation: in any substance/object, the particles inside it (atoms/molecules) constantly move in random directions and with random speeds (this motion is called brownian motion). as a result, the particles have some kinetic energy (which is proportional to the temperature of the substance).

explanation:

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total distance travelled = 60 miles

total time taken =1.5 hours

average speed = total distance / total time

60 / 1.5

= 40

therefore, average speed = 40 m/h

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