Question 29 - Problems - Chapter 2

Problem:

A messenger carries a package twelve city blocks north in 14 min 5 s.

There, she receives a second package, which she brings six blocks south in 6 min 28 s.

Finally, she gets a third package, which she brings 3 blocks north in 3 min 40 s.

The city block spacing is 81 m. what is her average speed?What is her average velocity?

Question:

a) What is her average speed?

b) What is her average velocity?

Solution:

$\bigtriangleup t_1 = 14m 5s$

$\bigtriangleup t_2= 6m 28s$

$\bigtriangleup t_3= 3m 40s$

One Block = 81m

$\bigtriangleup s_1 = 12x81m=972m$

$\bigtriangleup s_2 = -6x81m=-486m$

$\bigtriangleup s_2 = 3x81m=243m$

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The total displacement $\bigtriangleup s = \bigtriangleup s_1 + \bigtriangleup s_4 + \bigtriangleup s_5$

The average velocity:

$$ \overline v=\frac{\bigtriangleup s}{\bigtriangleup t} $$

Total distance $s = \Big|{{\bigtriangleup s_1}}\Big| + \Big|{\bigtriangleup s_2}\Big| + \Big|{\bigtriangleup s_3}\Big|$

The average speed is

$$ v = \frac{s}{t} $$

The problem is almost the same as problem Q028, so we can reuse the same program by just changing the values of the parameters.

import numpy as np
t1 = 14*60 + 5
t2 = 6*60 + 28
t3 = 3*60 + 40
d_s1 = 972
d_s2 = -486
d_s3 = 243
v_s = (np.abs(d_s1) + np.abs(d_s2) + np.abs(d_s3)) / (t1 + t2 + t3)
v_v = (d_s1 + d_s2 + d_s3) / (t1 + t2 + t3)
print(f'The average speed is: {v_s:.2f} m/s')
print(f'The average velocity is: {v_v:.2f} m/s')

The average speed is: 1.17 m/s
The average velocity is: 0.50 m/s