A bicyclist makes a trip that consists of three parts, each in the same direction (due north) along a straight road. During the first part, she rides for 22 minutes at an average speed of 6.60 m/s. During the second part, she rides for 36 minutes at an average speed of 5.40 m/s. Finally, during the third part, she rides for 8.0 minutes at an average speed of 11.4 m/s.
What is her average velocity for the trip?
"Average" speed results from dividing the total distance by the total time.
Using V = D/T
The distance covered during the 1st part is 22x6.6mi.
The distance covered during the 2nd part is 36x5.4mi.
The distance covered during the 3rd part is 8x14.4mi.
Therefore, her "average" speed is (D1 + D2 + D3)/(T1 + T2 + T3)
To find the average velocity for the trip, we can use the formula:
Average velocity = Total displacement / Total time
First, let's find the total displacement. Since the bicyclist is traveling in the same direction (due north) along a straight road, we can consider displacement as the algebraic sum of distances traveled.
In the first part, the distance covered can be calculated using the formula:
Distance = Speed * Time
So, in the first part, the distance covered is:
Distance1 = Speed1 * Time1
= 6.60 m/s * 22 minutes
Similarly, for the second part:
Distance2 = Speed2 * Time2
= 5.40 m/s * 36 minutes
And for the third part:
Distance3 = Speed3 * Time3
= 11.4 m/s * 8.0 minutes
Next, calculate the total displacement by adding the distances:
Total displacement = Distance1 + Distance2 + Distance3
Finally, calculate the average velocity using the formula mentioned earlier:
Average velocity = Total displacement / Total time
Since the total time is the sum of the times for each part of the trip:
Total time = Time1 + Time2 + Time3
Inputting the values and doing the calculations will give us the average velocity for the trip.