Martika is running a sprint. Her velocity, v(t), after time t is shown in the fo
ID: 2894300 • Letter: M
Question
Martika is running a sprint. Her velocity, v(t), after time t is shown in the following table. t is in seconds, and the velocity is in feet per second. A) Using the Left Endpoint Method with n = 4 subintervals, estimate the distance traveled over the first 8 seconds. The distance is about feet. B) Using the Right Endpoint Method with n = 4 subintervals, estimate the distance traveled over the first 8 seconds. The distance is about feet. C) Using the Midpoint Method with n = 4 subintervals, estimate the distance traveled over the first 8 seconds. The distance is about feet.Explanation / Answer
From the given question,
A)Left Endpoint Method:
v(0)=0, v(2)=7.3, v(4)=8, v(6)=8.2
Distance travelled= v(0)*2+v(2)*2+v(4)*2+v(6)*2
=2[ v(0)+v(2)+v(4)+v(6)]
=2(0+7.3+8+8.2)
=47 feet
The distance is about 47 feet.
B)Right Endpoint Method:
v(2)=7.3, v(4)=8, v(6)=8.2, v(8)=8.4
Distance travelled=v(2)*2+v(4)*2+v(6)*2+v(8)*2
=2[ v(2)+v(4)+v(6)+v(8)]
=2(7.3+8+8.2+8.4)
=63.8 feet
The distance is about 63.8 feet.
C)Midpoint Method:
v(1)=5.7, v(3)=7.8, v(5)=8.1, v(7)=8.3
Distance travelled=v(1)*2+v(3)*2+v(5)*2+v(7)*2
=2[ v(1)+v(3)+v(5)+v(7)]
=2(5.7+7.8+8.1+8.3)
=59.8 feet
The distance is about 59.8 feet.
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