3. -/10 points details my notes scalcet9 5.1.009.mi. the speed of a runner increased steadily during the…

3. -/10 points details my notes scalcet9 5.1.009.mi. the speed of a runner increased steadily during the first three seconds of a race. her speed at half - second intervals is given in the table. find lower and upper estimates for the distance (in ft) that she traveled during these three seconds. t (s) 0 0.5 1.0 1.5 2.0 2.5 3.0 v (ft/s) 0 6.7 9.2 15.5 18.8 19.4 20.2 lower ft upper ft submit answer

3. -/10 points details my notes scalcet9 5.1.009.mi. the speed of a runner increased steadily during the first three seconds of a race. her speed at half - second intervals is given in the table. find lower and upper estimates for the distance (in ft) that she traveled during these three seconds. t (s) 0 0.5 1.0 1.5 2.0 2.5 3.0 v (ft/s) 0 6.7 9.2 15.5 18.8 19.4 20.2 lower ft upper ft submit answer

Answer

Explanation:

Step1: Definir el intervalo de tiempo

El intervalo de tiempo $\Delta t = 0.5$ s.

Step2: Calcular la estimación inferior

Para la estimación inferior, usamos la velocidad más baja en cada sub - intervalo. [ \begin{align*} d_{lower}&=0\times0.5 + 6.7\times0.5+9.2\times0.5 + 15.5\times0.5+18.8\times0.5+19.4\times0.5\ &=0.5\times(0 + 6.7+9.2 + 15.5+18.8+19.4)\ &=0.5\times69.6\ &=34.8 \end{align*} ]

Step3: Calcular la estimación superior

Para la estimación superior, usamos la velocidad más alta en cada sub - intervalo. [ \begin{align*} d_{upper}&=6.7\times0.5+9.2\times0.5 + 15.5\times0.5+18.8\times0.5+19.4\times0.5+20.2\times0.5\ &=0.5\times(6.7+9.2 + 15.5+18.8+19.4+20.2)\ &=0.5\times89.8\ &=44.9 \end{align*} ]

Answer:

lower: $34.8$ ft upper: $44.9$ ft