A race car has a velocity of $v ( t ) = 600 \left( 1 - e ^ { - 1.6 t } \right) \frac { \mathrm { ft } } { \mathrm { s } }$ , t seconds after starting. Use a Riemann sum with n = 10 to estimate how far the car travels in the first 2 seconds. (Round your answer to the nearest whole number.)
A)780 feet
B) 713 feet
C) 895 feet
D) 576 feet
E) 846 feet

Question

A race car has a velocity of $v ( t ) = 600 \left( 1 - e ^ { - 1.6 t } \right) \frac { \mathrm { ft } } { \mathrm { s } }$ , t seconds after starting. Use a Riemann sum with n = 10 to estimate how far the car travels in the first 2 seconds. (Round your answer to the nearest whole number.) 
A)780 feet
B) 713 feet
C) 895 feet
D) 576 feet
E) 846 feet

Quizplus · Accepted Answer

The correct answer is A.The distance traveled is the integral of the velocity function. Using a Riemann sum with n = 10, we have:$$\int_0^2 600 (1 - e^{-1.6t}) dt \approx \sum_{i=1}^{10} 600 (1 - e^{-1.6t_i}) \Delta t$$where $t_i = 0.2i$.Evaluating the sum, we get:$$\sum_{i=1}^{10} 600 (1 - e^{-1.6t_i}) \Delta t \approx 780$$Therefore, the car travels approximately 780 feet in the first 2 seconds.

A Race Car Has a Velocity Of v(t)=600(1−e−1.6t)ftsv ( t ) = 600 \left( 1 - e ^ { - 1.6 t } \right) \frac { \mathrm { ft } } { \mathrm { s } }v(t)=600(1−e−1.6t)sft​

A Race Car Has a Velocity Of $v ( t ) = 600 \left( 1 - e ^ { - 1.6 t } \right) \frac { \mathrm { ft } } { \mathrm { s } }$