Problem 2.27 On a straight road with the +x axis chosen to point in the directio

Question

Problem 2.27 On a straight road with the +x axis chosen to point in the direction of motion, you drive for 6 hours at a constant 28 miles per hour, then in a few seconds you speed up to 70 miles per hour and drive at this speed for 1 hour. (a) What was the x component of average velocity for the 7-hour period, using the fundamental definition of average velocity, which is the displacement divided by the time interval? avg-x miles per hour (b) Suppose instead you use the formula Vavg,r - h do you calculate for the x component of average velocity? Vix t fx miles per hour (c) Why does the formula used in part (b) give the wrong answer? That formula isn't valid unless v changes at a constant rate (constant force). O That formula only applies at high speeds. O That formula can only be used for projectile motion, such as a baseball that has been hit.

Explanation / Answer

Dear student

Solution

The average speed in x-direction is given as

Distance covered while drive with 28 miles/hr in 6 hrs will be

Xi=velocity x time

Xi=28 x 6 =168 miles

Distance covered while drive with 70 miles/hr in 1 hr will be

Xf=70 x 1

Xf=70 miles

Total distance covered will be 238 miles in 7 hrs

Hence Average velocity will be

We have to use harmonic mean instead of simple mean

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