How do you find the instantaneous velocity for the particle whose position at time #t# is given by #s(t)=3t^2+5t# ?

Question

Evelyn Agard · Accepted Answer

by the derivative of the function we know that the derivative is a rate of change of a function and that velocity is the rate of change of position
,therefore, if we know the expression for position, its derivative will  be its velocity
therefore, #f'(x) = 6t + 5#

Emilia Aguilar · Answer

undefined To find the instantaneous velocity of a particle given its position function $ s(t) = 3t^2 + 5t $, you need to find the derivative of the position function with respect to time. The derivative of the position function $ s(t) $ with respect to time $ t $ will give you the instantaneous velocity function $ v(t) $. So, differentiate $ s(t) $ with respect to $ t $ to find $ v(t) $.

$ s(t) = 3t^2 + 5t $
$ v(t) = \frac{ds}{dt} $
$ v(t) = \frac{d}{dt}(3t^2 + 5t) $
$ v(t) = 6t + 5 $

Therefore, the instantaneous velocity of the particle at any time $ t $ is given by $ v(t) = 6t + 5 $.