Question

Jason drives due west with a speed of 41.0 mi/h for 30.0 min, then continues in the same direction with a speed of 51.0 mi/h for 2.00 h, then drives farther west at 35.0 mi/h for 12.0 min. What is Jason's average velocity?

Answer 1

The average velocity is 47.96 mi/h

Step-by-step explanation:

Well, there are many ways to calculate the average velocity, but the most complete one would be the following.

With the equations of Uniform Rectelinear Movement we can obtain the distance Jason has driven. We will use the same equation for each step.

`x(t)=x_(0) +v(t-t_(0))`

where x is the position,
`x_(0)` is the initial position (which we can pick as zero to simplify), v is the velocity, t is time and
`t_(0)` is the initial time (also picked as zero). In order to get the right answer we must use the same units, so we will change the minutes to hours, where 30 minutes are half an hour and 12 minutes are 0.2 hours

So, the distance will be

1. 
   `x(0.5h)=41 (mi)/(h) *0.5h=20.5mi`
2. 
   `x(2h)=51 (mi)/(h)*2h=102mi`
3. 
   `x(0.2h)=35 (mi)/(h)*0.2h=7mi`

Now that we have the partial distances, we use the formula for average velocity which is

`v_(av) =(x_(f)-x_(0))/(t_(f) -t_(0) )`

where
`x_(f)` is the final position (the sum of the distances) and
`t_(f)` is the total time Jason took.

Finally, we calculate the answer,

`v_(av)=((20.5mi+102mi+7mi)-0)/((0.5h+2h+0.2h)-0)=47.96(mi)/(h)`