Question

A motorist drives north for 36.0 minutes at 96.0 km/h and then stops for 15.0 minutes. He then continues north, traveling 130 km in 2.20 h. (a) What is his total displacement? km

(b) What is his average velocity? km/h

Answer 1

a)
`d=187.6km`

b)
`v=61.5km/h`

Step-by-step explanation:

First we convert our minutes to hours so we work always in the same units.

`36min=36min((1h)/(60min))=0.6h`

`15min=15min((1h)/(60min))=0.25h`

Where we used the fact that 1 hour are 60 min, thus the multiplying factor is equal to 1 (not altering the time, just changing the units).

a) On the first part the motorist travels a distance
`d_1=v_1t_1=(96km/h)(0.6h)=57.6km`, and on the second part he travels
`d_2=130km`.

The total displacement is
`d=d_1+d_2=57.6km+130km=187.6km`

b) The average velocity is the relation between the total displacement and the time taken to cover it. Our total time is t=0.6h+0.25h+2.2h=3.05h, thus we have:

`v=(187.6km)/(3.05h)=61.5km/h`