Answer:
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.
