Question

t(seconds) 0 1 2 3 4 5
s(feet) 0 10 32 70 119 178

Find the average velocity for the time period beginning when t=2 and lasting

1.3s

Estimate the instantaneous velocity when t=2

Answer 1

0 0
1 10
2 32
3 70
4 119
5 178

Lets approximate this x versus time curve with a parabola between t = 2 and t = 4
x = a t^2 + b t + c

32 = 4 a + 2 b + c
70 = 9 a + 3 b + c
119 = 16 a + 4 b + c

solve for a, b and c
then find x at t = 3.3
subtract x at 2 which is 32
divide by 1.3
that is an approximation for average speed between t = 2 and t = 3.3

for speed at t = 2
dx/dt = 2 a t + b
or just approximate slope at two by
(x at 3 - x at 1)/2 seconds
= (70-10)/2 = 30 ft/s