On a straight road with the +x axis chosen to point in the direction of motion, you drive for 3 hours at a constant 20 miles per hour, then in a few seconds you speed up to 70 miles per hour and drive at this speed for 1 hour. What was the x component of average velocity for the 4-hour period, using the fundamental definition of average velocity, which is the displacement divided by the time interval? vavg, x = miles per hour Suppose instead you use the formula vavg, x = vix + vfx / 2. What do you calculate for the x component of average velocity? vavg. x = vux + vfx/2 = miles per hour Why does the formula used in part (b) give the wrong answer? That formula can only be used for projectile motion, such as a baseball that has been hit. That formula isn't valid unless vx changes at a constant rate (constant force). That formula only applies at high speeds.

Explanation:

First part

I drove for 3hours at 20miles/hour

Second part

In a few seconds, acceleration occurs and I increased my speed to 70miles/hour and i drove for 1hour.

Assume the time of acceleration is

1. Average velocity for the 4 hour period i travelled

Average velocity is given as

Average velocity = total displacement / total time take

In this case, total time for the journey is 4hours

Displace for first part.

Velocity=displacement/time

Displacement = velocity ×time

Velocity =20miles/hr and time is 3 hours for the first part,

Then, displacement = 20×3

Displacement =60miles

For the second, part

Displacement= 70×1=70miles

Since both displacement are positive x direction, then

Therefore, total displacement is 70i+60i= 130i miles

Then,

Average Velocity =d/t

Average Velocity=130/4

Average velocity = 32.5miles/hour.

Average velocity is 32.5miles/hour in the positive x direction.

2. Using the formula given the questions,

Vavg=(Vx i+ Vx j)/2

Since there is no y component of the velocity, then Vy=0

The car is moving in the same direction, positive x direction

First part 20i miles/hour

Second part 70i miles/hour.

Then, Vx=20i+70i=90i miles/hour

Vavg=(Vx i +Vy j)/2

Vavg=(90i+0)/2

Vavg=45i miles/hour

The answers are different and this is due to the fact that the second aspect did not calculate the average velocity

The formular in part b gives the wrong answer because it doesn't considered the time they use in traveling assuming they have travelled at 2hours each then the part b will be right.

The formula can be use when the time taken to travel each different aspects of the journey are equal.

E.g, let assume 2 hours each

Then, D1=V×t= 20×2=40miles

D2=V×t, =70×2=140miles

Then A.V=(D1+D2)/4

A.V=(40+140)/4

A.V=180/4

A.V=45miles/hours.

This is equal to the average velocity formula.

So they can only be equal when they travel at equal intervals of time.

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