view policies current attempt in progress a car starts moving at time t = 0 and goes faster and faster. its…

view policies current attempt in progress a car starts moving at time t = 0 and goes faster and faster. its velocity is shown in the following table. estimate how far the car travels during the 12 seconds. t (seconds) 0 3 6 9 12 velocity (ft/sec) 0 12 26 46 77 an underestimate for the distance traveled = an overestimate for the distance traveled = a better estimate is the average of the above: distance traveled ≈ etextbook and media attempts: 0 of 4 used sub save for later

view policies current attempt in progress a car starts moving at time t = 0 and goes faster and faster. its velocity is shown in the following table. estimate how far the car travels during the 12 seconds. t (seconds) 0 3 6 9 12 velocity (ft/sec) 0 12 26 46 77 an underestimate for the distance traveled = an overestimate for the distance traveled = a better estimate is the average of the above: distance traveled ≈ etextbook and media attempts: 0 of 4 used sub save for later

Answer

Explanation:

Step1: Calculate underestimate

We use the left - hand sum. The time intervals are $\Delta t=3$ seconds. The underestimate of the distance $d_{under}$ is given by the sum of the product of the velocity at the left - hand endpoint of each sub - interval and the time interval. $d_{under}=0\times3 + 12\times3+26\times3 + 46\times3$ $d_{under}=(0 + 12+26 + 46)\times3$ $d_{under}=84\times3=252$ feet.

Step2: Calculate overestimate

We use the right - hand sum. The overestimate of the distance $d_{over}$ is given by the sum of the product of the velocity at the right - hand endpoint of each sub - interval and the time interval. $d_{over}=12\times3+26\times3 + 46\times3+77\times3$ $d_{over}=(12 + 26+46 + 77)\times3$ $d_{over}=161\times3 = 483$ feet.

Step3: Calculate better estimate

The better estimate is the average of the underestimate and overestimate. $d=\frac{d_{under}+d_{over}}{2}=\frac{252 + 483}{2}=\frac{735}{2}=367.5$ feet.

Answer:

An underestimate for the distance traveled = 252 An overestimate for the distance traveled = 483 Distance traveled $\approx$ 367.5