Question

The table below shows the velocity of a car, in km per minute at different times, in minutes. What is the upper estimate of how far the car went during the twenty minutes?

t 0 5 10 15 20
v(t) 0.5 1 1 1.5 2


Select one:

a.
30 km

b.
27.5 km

c.
4.5 km

d.
5 km

e.
20 km

Answer 1

The upper estimate of the distance the car traveled during twenty minutes is approximately 28.75 km, so the closest option is b. 27.5 km.

To estimate the distance traveled by the car, we can use the trapezoidal rule for integration. The formula is given by:

`\[ \text{Distance} \approx (h)/(2) \left[ f(t_0) + 2f(t_1) + 2f(t_2) + \ldots + 2f(t_(n-1)) + f(t_n) \right] \]`

where h is the time interval and f(t) is the velocity at time t . In this case,
h = 5 minutes.

`\[ \text{Distance} \approx (5)/(2) \left[ 0.5 + 2(1) + 2(1) + 2(1.5) + 2(2) \right] \]`

`\[ \text{Distance} \approx (5)/(2) \left[ 0.5 + 2 + 2 + 3 + 4 \right] \]`

`\[ \text{Distance} \approx (5)/(2) * 11.5 \]`

`\[ \text{Distance} \approx 28.75 \]`

The upper estimate of how far the car went during the twenty minutes is approximately 28.75 km. Therefore, the closest option is:

b. 27.5 km.