current attempt in progress\na car is traveling at 82 feet per second (approximately 55 miles per hour) and…

current attempt in progress\na car is traveling at 82 feet per second (approximately 55 miles per hour) and slows down as it passes through a busy intersection. the car’s velocity is shown in the following table.\ntime since brakes applied (seconds) 0 3 6 9 12\nvelocity (ft/sec) 82 62 47 32 22\n(c) use a right sum to approximate the total distance the car has traveled over the 12 - second interval.\ndistance traveled = feet.\n(d) is your answer in part (c) a lower or upper estimate?\nhow can you tell?\nchoose one \nbecause the velocity is decreasing, so\nchoose one

current attempt in progress\na car is traveling at 82 feet per second (approximately 55 miles per hour) and slows down as it passes through a busy intersection. the car’s velocity is shown in the following table.\ntime since brakes applied (seconds) 0 3 6 9 12\nvelocity (ft/sec) 82 62 47 32 22\n(c) use a right sum to approximate the total distance the car has traveled over the 12 - second interval.\ndistance traveled = feet.\n(d) is your answer in part (c) a lower or upper estimate?\nhow can you tell?\nchoose one \nbecause the velocity is decreasing, so\nchoose one

Answer

Explanation:

Step1: Identify the sub - intervals and $\Delta t$

The time interval is from $t = 0$ to $t=12$ seconds, and we have sub - intervals of $\Delta t=3$ seconds.

Step2: Set up the right - sum formula for distance

The right - sum formula for distance $D$ given velocity $v(t)$ is $D=\sum_{i = 1}^{n}v(t_i)\Delta t$, where $t_i$ are the right - hand endpoints of the sub - intervals.

Step3: Calculate the right - sum

We have $n = 4$ sub - intervals. The right - hand endpoints are $t_1 = 3,t_2=6,t_3 = 9,t_4=12$. $D=v(3)\times3+v(6)\times3+v(9)\times3+v(12)\times3$ $D = 62\times3+47\times3+32\times3+22\times3$ $D=(62 + 47+32+22)\times3$ $D=(163)\times3$ $D = 489$

Step4: Determine if it's a lower or upper estimate

Since the velocity function $v(t)$ is decreasing, a right - sum is a lower estimate. Because when we use a right - sum for a decreasing function, we are using the smallest velocity value in each sub - interval to approximate the distance traveled in that sub - interval.

Answer:

(c) 489 (d) Lower estimate; we are using the smallest velocity value in each sub - interval for the approximation since the velocity is decreasing.