The position function s of a point P moving on a coordinate line l is given, with t in seconds and s(t) in centimeters.
(a) Find the average velocity of P in the following interval [1, 1.2].
(b) Find the velocity of P at t = 1.
s(t) = 4t^2 + 3t
The position function s of a point P moving on a coordinate line l is given, with t in seconds and s(t) in centimeters.
(a) Find the average velocity of P in the following interval [1, 1.2].
(b) Find the velocity of P at t = 1.
s(t) = 4t^2 + 3t
Good!
The velocity of the particle at t=1 is equal to the slope of the s(t) curve at t=1. I suggested calculating the derivative to find that slope - have you taken any calculus classes where you have learned about derivatives? If not, then you could plot the graph of s=4^2+3t and use a straight edge to estimate its slope at t=1. Alternatively, you could use the same approach as in part (a) to find the average velocity between two points that are very close to t=1; for example if you calculate the average velocity over the interval t= (0.99, 1.01) you will get a very good approximation of the actual velocity at t=1.
Thank you ebaines for the detailed explanation. Yes, I know how to find the slope using the Derivative.
When I find the derivative of 4t^2 + 3t, I get 8t + 3.
If my calculations went correctly, the Velocity at t = 1, might be 8(1) + 3 = 11.