Hey physics instant velocity ques

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To find the instantaneous velocity of an arrow shot upward on the moon with a height function h=58t-0.83t^2, the first derivative represents the velocity. Since derivatives are not allowed in this calculus class, an alternative method involves calculating the slope using average velocities over small time intervals. By selecting values close to t=1 second, one can approximate the instantaneous velocity. The slope formula, m = Δh/Δt, can be applied to these values to find the desired result. This approach allows for understanding without directly using derivatives.
lilman7769
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If an arrow is shot upward on the moon with a velocity of 58m/s, its height in meters after t seconds is given by h=58t-0.83t^2

find the instantaneous velocity after one second...can u post ur work?? and explain this to me...thx in advance...
 
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Instant Velocity is

\vec{V} = \frac{d \vec{r}}{dt}

If you have this formula, then the first derivative is speed. For velocity, remember to put the j, because it's 1D motion in the y-axis.

h=58t-0.83t^2
 
its for a calculus class and we arent allowed to use derivtives yet...so for that forula u gave me what number would i plug in? I am kinda confused...i did a table of values with time intervals to average velocity but the whole one second i don't understand...can u show me like an answer...im sorry ur rules are u not doing my hmk...i seriously have tried i just don't understand...
 
You could graph that function, and pick really close values for time and h, to calculate the slope.

The First derivative is the slope.

Slope formula
m = \frac{\Delta h}{\Delta t}
 

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