the table below shows the velocity of an object (cm/sec) at each sec as it moves along a track for 10 sec…

the table below shows the velocity of an object (cm/sec) at each sec as it moves along a track for 10 sec. estimate the distance traveled using ten subintervals of length 1 sec with left - endpoint values. estimate the distance traveled using ten subintervals of length 1 sec with right - endpoint values.\ntime (sec) 0 1 2 3 4 5 6 7 8 9 10\nvelocity (cm/sec) 0 5 11 14 24 36 24 15 8 5 0\nthe distance traveled using ten subintervals of length 1 sec with left - endpoint values is cm\n(simplify your answer.)

the table below shows the velocity of an object (cm/sec) at each sec as it moves along a track for 10 sec. estimate the distance traveled using ten subintervals of length 1 sec with left - endpoint values. estimate the distance traveled using ten subintervals of length 1 sec with right - endpoint values.\ntime (sec) 0 1 2 3 4 5 6 7 8 9 10\nvelocity (cm/sec) 0 5 11 14 24 36 24 15 8 5 0\nthe distance traveled using ten subintervals of length 1 sec with left - endpoint values is cm\n(simplify your answer.)

Answer

Explanation:

Step1: Recall the left - endpoint Riemann sum formula

The formula for the left - endpoint Riemann sum for approximating the distance $d$ given velocity $v(t)$ over $n$ subintervals of width $\Delta t$ is $d\approx\sum_{i = 0}^{n - 1}v(t_i)\Delta t$. Here, $n = 10$ and $\Delta t=1$ sec.

Step2: Identify the left - endpoint velocities

The left - endpoint velocities for the 10 subintervals of length 1 sec are $v(0),v(1),v(2),\cdots,v(9)$. From the table, the velocities are $0,5,11,14,24,36,24,15,8,5$.

Step3: Calculate the sum

$d=\sum_{i = 0}^{9}v(t_i)\Delta t=(0 + 5+11+14+24+36+24+15+8+5)\times1$. $d=0 + 5+11+14+24+36+24+15+8+5=142$.

Answer:

142