How to Find Instantaneous Velocity at a Specific Time?

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To find the instantaneous velocity at t=1, the formula v(1) = [h(1+Δt) - h(1)]/Δt is used. The value of h(1) is given as 24, and the calculated instantaneous velocity is v(1) = -8 ft/sec. To determine h(1+Δt), substitute (1+Δt) into the height function h(t) = 16 + 24t - 16t². After expanding the equation and performing algebraic manipulation, the solution aligns with the teacher's result of v(1) = -8 - 16tΔ. Understanding this process is crucial for accurately calculating instantaneous velocity.
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Homework Statement



Find the instantaneous velocity at t=1 by computing v(1)= [h(1+\Deltat)-h(1)]/\Deltat

I found that v(1)= -8ft/sec. Also I know h(1)=24 but i don't understand how to manipulate the h(1+\Deltat) to get the solution.

Homework Equations



h(t)=16+24t-16t2

The Attempt at a Solution



The solution the teacher gave is v(1)=-8-16t\Delta
 
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What's h(1+dt)? Substitute (1+dt) into the h(t) equation.. and put everything in the v(1)= [h(1+dt)-h(1)]/dt equation. If you expand the equation and do some algebra you will eventually get the answer
 

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