Question

(1 point) A radar gun was used to record the speed of a runner during the first 5 seconds of a race (see table). Use Simpson's rule to estimate the distance the runner covered during those 5 seconds. 1 1.5 2.5 3 3.5 4 4.5 5 t(s) 0 0.5 v (ft/s) 0 2.3 4.7 6 7.6 | 7.85 | 7.95 7.95 | 9.7 9.8 | 10.65 10.65 Estimated distance:

Answer 1

we know that

Simpson’s Rule is a numerical method that approximates the value of a definite integral by using quadratic functions.

The coefficients in Simpson’s Rule have the following pattern:

1,4,2,4,2...

we have n+1 poins

Remember that

The distance is equal to multiply the speed by the time

distance is equal to

(Dx/3)*{V(0)+4V(0.5)+2V(1.0)+4V(1.5)+2V(2.0)+4V(2.5)+2V(3.0)+4V(3.5)+2V(4.0)+4V(4.5)+V(5.0)}

substitute the given values

Dx=0.5

(0.5/3)*{0+4(2.3)+2(4.7)+4(6)+2(7.6)+4(7.85)+2(7.95)+4(9.7)+2(9.8)+4(10.65)+(10.65)}

(0.5/3)*{0+9.2+9.4+24+15.2+31.4+15.9+38.8+19.6+42.6+10.65}

(0.5/3)*{216.75}

d=36.125 ft