Question

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 7.2 m/s. During the second part, she rides for 36 minutes at an average speed of 5.1 m/s. Finally, during the third part, she rides for 8.0 minutes at an average speed of 13 m/s. (a) How far has the bicyclist traveled during the entire trip? (b) What is her average velocity for the trip? (Ans: a)26.7km, b) 6.74m/s)

Answer 1

a

The total distance traveled is
`D = 26760 \ m`

b

The average velocity is
`v_(avg) = 6.8 \ m/s`

Step-by-step explanation:

From the question we are told that

The time taken for first part
`t_1 = 22 \ minutes = 22*60 = 1320 \ s`

The speed for the first part is
`v_1 = 7.2 \ m/s`

The time taken for second part is
`t_2 = 36 \ minutes = 2160 \ s`

The speed for the second part is
`v_2 = 5.1 \ m/s`

The time taken for third part is
`t_3 = 8 \ minutes = 480 \ s`

The speed for the third part is
`v_3 = 13 m/s`

Generally

`distance(D) = velocity * time`

Therefore the total distance traveled is

`D = (v_1 * t_1) + (v_2 * t_2 ) + (v_3 * t_3)`

substituting values

`D = (7.2 * 1320) + (5.1 * 2160) + (13 * 480)`

`D = 26760 \ m`

Generally the average velocity is mathematically represented as

`v_(avg) = (D)/(t_(total))`

Where
`t_(total)` is the total time taken which is mathematically represented as

`t_(total) = 1320 + 2160 + 480`

`t_(total) =3960\ s`

The average velocity is

`v_(avg) = (26760)/(3960)`

`v_(avg) = 6.8 \ m/s`