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given s(t)=3t +5t+3, find the instantaneous velocity when t i= 5.
ds/dt is the velocity.
Assuming you meant
s(t) = 3t^2 + 5t + 3
ds/dt = 6t + 5
so plug in t=5.
Hi Steve, can you show me step by step how to factor this, because my numbers compared to the correct numbers are way too low and I don't know what I'm doing wrong.
how to factor what?
ds/dt at t=5 is just
6*5+5 = 35
To find the instantaneous velocity of a function at a specific time, you need to take its derivative with respect to time and then evaluate it at the given time.
So, let's start by finding the derivative of the function s(t) = 3t + 5t^2 + 3. The derivative of a term with a constant coefficient is 0, and the derivative of t^n is n * t^(n-1). Applying these rules, we get:
s'(t) = 3 + 2 * 5t + 0
= 3 + 10t
Now, to find the instantaneous velocity, we need to substitute the given time t = 5 into the derivative s'(t):
s'(5) = 3 + 10 * 5
= 3 + 50
= 53
Therefore, the instantaneous velocity when t = 5 is 53 units per time.