Question

1. a train travels 120 km east at a constant velocity of 80 km/h. the train then stops for 30 minutes. finally, it continues east for another 160 km at a velocity of 100 km/h. what is the total time for the journey in hours? 4. a car travels a total distance of 400 km in 5.0 hours. for the first 2.0 hours, the car travels at a constant speed of 70 km/h. what was the constant speed of the car for the last 3.0 hours of the trip? 5. anne starts at the east end of a 20 - mile - long path and walks west at a constant velocity of 3.0 mi/h. at the exact same time, her friend beth starts at the west end of the path and walks east at a constant velocity of 2.0 mi/h. how much time will pass before they meet?

Explanation:

3.

Step1: Calculate time for first - part of train journey

Use the formula $t=\frac{d}{v}$, where $d = 120$ km and $v = 80$ km/h. So $t_1=\frac{120}{80}=1.5$ h.

Step2: Add the stop - time

The train stops for 30 minutes or 0.5 h. So the accumulated time is $t_{acc}=t_1 + 0.5=1.5 + 0.5=2$ h.

Step3: Calculate time for second - part of train journey

Use the formula $t=\frac{d}{v}$ again, with $d = 160$ km and $v = 100$ km/h. So $t_2=\frac{160}{100}=1.6$ h.

Step4: Calculate total time

The total time $t_{total}=t_{acc}+t_2=2 + 1.6=3.6$ h.

Step1: Calculate distance traveled in first 2 hours

Use the formula $d = vt$, where $v = 70$ km/h and $t = 2$ h. So $d_1=70\times2 = 140$ km.

Step2: Calculate distance traveled in last 3 hours

The total distance $d_{total}=400$ km. So $d_2=d_{total}-d_1=400 - 140=260$ km.

Step3: Calculate speed in last 3 hours

Use the formula $v=\frac{d}{t}$, with $d = d_2 = 260$ km and $t = 3$ h. So $v=\frac{260}{3}\approx86.67$ km/h.

Step1: Consider the relative - velocity

Since Anne and Beth are walking towards each other, the relative velocity $v = v_{Anne}+v_{Beth}=3.0+2.0 = 5.0$ mi/h.

Step2: Calculate the meeting time

Use the formula $t=\frac{d}{v}$, where $d = 20$ miles and $v = 5.0$ mi/h. So $t=\frac{20}{5}=4$ h.

Answer:

$3.6$ h

4.