----A car travels along a straight line at a constant speed of 45.0 mi/h for a d
ID: 2286827 • Letter: #
Question
----A car travels along a straight line at a constant speed of 45.0 mi/h for a distance d and then another distance d in the same direction at another constant speed. The average velocity for the entire trip is 26.5 mi/h.
(a) What is the constant speed with which the car moved during the second distance d?
1 mi/h
(b) Suppose the second distance d were traveled in the opposite direction; you forgot something and had to return home at the same constant speed as found in part (a). What is the average velocity for this trip?
2 mi/h
(c) What is the average speed for this new trip?
3 mi/h
(a) What is her average speed over the entire trip?
Use the symbol d to represent the distance between points A and B. The average speed is defined as the total distance traveled divided by the total time interval. m/s
(b) What is her average velocity over the entire trip?
The average velocity is defined as the displacement divided by the time. What is the displacement for the entire trip? m/s
Explanation / Answer
E1: v1=43.0 mi/h
E2: d = v1*t1 [1st distance, constant speed v1]
E3: d = v2*t2 [2nd distance, another constant speed v2]
E4: v3=33.5 mi/h
E5: 2d = v3*(t1+t2) [double distance, average velocity v3]
Combine E2 and E3 and calculate t2
v2*t2 = v1*t1
E6: t2 = v1*t1/v2
In E5, substitute t2 with t2 from E6 and d with d from E2
2*v1*t1 = v3*(t1 + v1*t1/v2)
2*v1*t1 = v3*t1 + v3*v1*t1/v2
2*v1*t1 - v3*t1 = v3*v1*t1/v2
(2*v1-v3)*t1 = v3*v1*t1/v2
2*v1-v3 = v3*v1/v2
or
E7: v2 = v3*v1/(2*v1-v3)
In E7 substitute v1 with v1 from E1 and v3 with v3 from E4
v2 = 33.5*43 / (2*43 - 33.5)
v2 = 27.438095 mi/h
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b)
There are 2 options:
b1) if you take distance d as a "scalar" then you traveled d+d = 2d and the velocity is the same as in a)
b2) if you take distance d as a "vector" then you traveled d-d = 0 and the velocity is 0
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