Question

1. a car moves with a steady speed of 74 km/h for 35.0 min, then 83 km/h for 18.0 minutes.

a) what was the total distance travelled during the whole trip?
b) what is the average speed for the whole trip?

Explanation:

Step1: Calculate distance of first - part

First, convert 35.0 minutes to hours. Since 1 hour = 60 minutes, 35.0 minutes=$\frac{35}{60}=\frac{7}{12}$ hours. Using the formula $d = vt$ (distance = speed×time), for the first - part with speed $v_1 = 74$ km/h and time $t_1=\frac{7}{12}$ h, the distance $d_1=74\times\frac{7}{12}=\frac{518}{12}=\frac{259}{6}$ km.

Step2: Calculate distance of second - part

Convert 10.0 minutes to hours. 10.0 minutes = $\frac{10}{60}=\frac{1}{6}$ hours. With speed $v_2 = 93$ km/h and time $t_2=\frac{1}{6}$ h, using $d = vt$, the distance $d_2=93\times\frac{1}{6}=\frac{93}{6}$ km.

Step3: Calculate total distance

The total distance $d=d_1 + d_2=\frac{259}{6}+\frac{93}{6}=\frac{259 + 93}{6}=\frac{352}{6}=\frac{176}{3}\approx58.67$ km.

Step4: Calculate total time

The total time $t=t_1 + t_2=\frac{7}{12}+\frac{1}{6}=\frac{7 + 2}{12}=\frac{9}{12}=\frac{3}{4}$ hours.

Step5: Calculate average speed

Using the formula $v_{avg}=\frac{d}{t}$, with $d=\frac{176}{3}$ km and $t=\frac{3}{4}$ h, $v_{avg}=\frac{\frac{176}{3}}{\frac{3}{4}}=\frac{176}{3}\times\frac{4}{3}=\frac{704}{9}\approx78.22$ km/h.

Answer:

a) $\frac{176}{3}$ km
b) $\frac{704}{9}$ km/h