Question

A particle moves along a straight line with equation of motion s = t^2 + 3t + 1, determine the velocity at t=10 seconds.

Answer 1

velocity at time t = ds/dt
find ds/dt and plug in t=10

Answer 2

can you demonstrate using difference quotient?

Answer 3

if s = a t^n
ds/dt = an t^(n-1)

Answer 4

yes, what cwrw posted is just the power rule.

Answer 5

Can you find the derivative?
Just apply the power rule to each of the terms.
To, \(\large\color{black}{ \tt t^2 }\) , \(\large\color{black}{ \tt 3t }\) and derivative of \(\large\color{black}{ \tt 1 }\), just like derivative of any other constant, is zero.

Answer 6

@cleetus779 ?

Answer 7

Anything you don't understand? please reply don't be scilent.

Answer 8

Simply speaking, you have
\(\large\color{black}{ \tt s(t) = t^2 + 3t + 1 }\)

And you need, \(\large\color{black}{ \tt s'(10) }\)