Question

Suppose the odometer on our car is broken and we want to estimate the distance driven over a 30 second time interval. We take the speedometer readings every five seconds and record them in the following table. Time (s) 0 5 10 15 20 25 30 Velocity (mi/h) 16 21 23 26 33 30 28 In order to have the time and the velocity in consistent units, let's convert the velocity readings to feet per second (1 mi/h = 5280 3600 ft/s). (Roun

Answer 1

Distance traveled in 30 sec will be 1274.75 feet

Step-by-step explanation:

We have given reading of velocity in mi per hour is

Velocity in mi per hour 16 21 23 26 33 30 28

Interval of time 0 5 10 15 20 25 30

And we know that 1 mi = 5280 feet and 1 hour = 3600 sec

So 1 mi/hr
`=(5200)/(3600)=1.44ft/sec`

Now velocity in ft/sec 23.11 30.24 33.12 37.44 47.52 43.20 40.32

Time gap between each interval is 5 sec

So distance traveled will be
`=(23.11* 5+30.24* 5+33.12* 5+37.44* 5+47.52* 5+43.2* 5+40.32* 5)=1274.75feet`

Answer 2

Let say for every 5 s of time interval the speed will remain constant

so it is given as

v(mi/h) 16 21 23 26 33 30 28

now we have to convert the speed into ft/s as it is given that 1 mi/h = 5280/3600 ft/s

so here we will have

v(ft/s) 23.5 30.8 33.73 38.13 48.4 44 41.1

now for each interval of 5 s we will have to find the distance cover for above interval of time

`d = v * t`

`d = (23.5 + 30.8 + 33.73 + 38.13 + 48.4 + 44 + 41.1) * 5`

`d = 1298.1 ft`

so here it will cover 1298.1 ft distance in 30 s interval of time