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You decide to travel by car for your holiday visits this year. You leave early in the morning to avoid congestion on the roads. This enables you to drive at a comfortable speed of v1=65.9 mphfor t1=3.22 hours. However, after this time, you unexpectedly come to a stop for tstop=42.1 min. Traffic starts moving again and you finish your travel at v2=57.6 mph for an additional t2=0.95 hours. How far did you travel on this trip? What was your average speed? There are 1609 meters in one mile.

Respuesta :

Answer:

[tex]d_t=266.918\ miles[/tex] is the total distance of the trip travelled.

[tex]s_{avg}=54.7895\ mph[/tex] is the average speed of the journey

Explanation:

Given:

  • duration of first interval, [tex]t_1=3.22\ hr[/tex]
  • speed during the first interval, [tex]v_1=65.9\ mph[/tex]
  • duration of stoppage, [tex]t_0=42.1\ min=0.7017\ hr[/tex]
  • duration of second interval, [tex]t_2=0.95\ hr[/tex]
  • speed during second interval, [tex]v_2=57.6\ mph[/tex]

Now the total distance travelled:

[tex]\rm distance=speed\times time[/tex]

[tex]d_t=v_2.t_2+v_1.t_1[/tex]

[tex]d_t=57.6\times 0.95+65.9\times 3.22[/tex]

[tex]d_t=266.918\ miles[/tex]

The average speed:

[tex]\rm speed_{avg}=\frac{total\ distance}{total\ time\ taken}[/tex]

[tex]s_{avg}=\frac{d_t}{(t_0+t_1+t_2)}[/tex]

[tex]s_{avg}=\frac{266.918}{(0.7017+3.22+0.95)}[/tex]

[tex]s_{avg}=54.7895\ mph[/tex]