A rock is dropped from a height of 64ft. Its height above ground at time t seconds later is given by s(t)=−16t2+64 for 0≤t≤2. Find its instantaneous velocity 1 second after it is dropped using the limit definition of a derivative. Do not include units in your answer.

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Asked Sep 30, 2019
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A rock is dropped from a height of 64ft. Its height above ground at time t seconds later is given by s(t)=−16t2+64 for 0≤t≤2. Find its instantaneous velocity 1 second after it is dropped using the limit definition of a derivative. Do not include units in your answer.

 

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Step 1

Consider the model function that represents the height above the ground as s(...

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rs'(1) lim )=s(1) dt ds The instantaneous velocity at t=1 is t-1 t=1 Substitute the s(t) and s(1) in the limit and evaluate it as follows $(1) lim ()-s(1) t1 t-1 .(-16 +64)-(-16(1+64) lim t-1 -16 64 6416 =lim t-1 t1

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