Question

1. a car moves with a steady speed of 74 km/h for 35.0 min, then 65 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: Convert time to hours

First convert 35.0 min and 18.0 min to hours. 35.0 min=$\frac{35.0}{60}$ h, 18.0 min=$\frac{18.0}{60}$ h.

Step2: Calculate distance for first - part

Use the formula $d = vt$. For the first part, $v_1 = 74$ km/h and $t_1=\frac{35.0}{60}$ h, so $d_1=v_1t_1 = 74\times\frac{35.0}{60}$ km.

Step3: Calculate distance for second - part

For the second part, $v_2 = 115$ km/h and $t_2=\frac{18.0}{60}$ h, so $d_2=v_2t_2 = 115\times\frac{18.0}{60}$ km.

Step4: Calculate total distance

$d=d_1 + d_2=74\times\frac{35.0}{60}+115\times\frac{18.0}{60}=\frac{74\times35.0 + 115\times18.0}{60}=\frac{2590+2070}{60}=\frac{4660}{60}\approx77.7$ km.

Step5: Calculate total time

$t=t_1 + t_2=\frac{35.0 + 18.0}{60}=\frac{53.0}{60}$ h.

Step6: Calculate average speed

Use the formula $v_{avg}=\frac{d}{t}$. $v_{avg}=\frac{\frac{4660}{60}}{\frac{53.0}{60}}=\frac{4660}{53.0}\approx88.0$ km/h.

Answer:

a) The total distance travelled is approximately 77.7 km.
b) The average speed for the whole trip is approximately 88.0 km/h.