Posted by **Helen** on Saturday, October 27, 2012 at 4:40pm.

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

- math -
**Damon**, Saturday, October 27, 2012 at 5:17pm
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

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