On a straight road with the x axis chosen to point in the di

On a straight road with the +x axis chosen to point in the direction of motion, you drive for 5 hours at a constant 40 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 6-hour period, using the fundamental definition of average velocity, which is the displacement divided by the time interval? V_avg,x = miles per hour Suppose instead you use the formula v_avg, x = v_ix + c_fx /2 What do you calculate for the x component of average velocity? Why does the formula used in part (b) give the wrong answer? That formula only applies at high speeds. That formula isn\'t valid unless v_x changes at a constant rate (constant force). That formula can only be used for projectile motion, such as a baseball that has been hit.

Solution

Total distance travelled S = d1+d2 , d1 distance travelled in first 5 hours : d2 distaance travelled in last hour

                  S = 40m/h * 5hr + 70mi/h * 1hr = 270 mi

time taken to reach 270 miles is 6 hours ,

            so the average velocity

                         Vavg = total distance / total time = 270 / 6 = 45mi/hr

a) since the velocity is along +ve x direction only Vx = +45mi/hr for 6 hour period

b) Vix = 40mi/hr and Vfx = 70mi/hr Vavg = 40+70 / 2 = 55 mi/hr

c)the formula is note valid unless Vx changes at a constant rate

it mean the car has to start with intial velocity 40 mi/hr and reach final velocity 70 mi/hr in a duration of 6 hrs