Average Speed Problems Practice - Master Motion Calculations

Let's first remind ourselves of the formula for finding velocity:

$V=\frac{x}{t}$

$x$ = distance
$t$ = time
$V$ = velocity

Then substitute the data into the formula:

$V=\frac{210+40+0+250}{3+1+2+2.5}$

Calculate accordingly to get:

$V=\frac{500}{8.5}=58.82$

Therefore, the average velocity is 58.82.

In the first stage, we want to find the distance the truck traveled in its total journey,

We will use the data we already have,

78 km/h for two hours of driving and 85 km/h for an additional hour and a half.

78*2+85*1.5=

156+127.5=

283.5 km

Now, we want to discover the total duration of the journey.

We know there were two hours of driving, a quarter-hour break, and another hour and a half of driving,

Meaning:

2+0.25+1.5=

3.75 hours

Now, we'll divide the travel distance by the number of hours

285/3.75=

75.6 km/h

And that's the average speed!

Let's begin solving this problem by following the outlined steps:

• **Step 1**: Convert the time to seconds.
  Running time for each interval = $2 \text{ minutes} = 2 \times 60 = 120 \text{ seconds}$.
  Rest time = $1 \text{ minute} = 60 \text{ seconds}$.
• **Step 2**: Calculate the distance covered during each running interval.
  Distance for the first interval, $d_1 = 2 \text{ m/s} \times 120 \text{ s} = 240 \text{ meters}$.
  Distance for the second interval, $d_2 = 2 \text{ m/s} \times 120 \text{ s} = 240 \text{ meters}$.
• **Step 3**: Determine the total distance and total time.
  Total distance, $D = d_1 + d_2 = 240 \text{ m} + 240 \text{ m} = 480 \text{ meters}$.
  Total time, $T = 120 \text{ s} + 60 \text{ s} + 120 \text{ s} = 300 \text{ seconds}$.
• **Step 4**: Calculate the average speed. $\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{480 \text{ m}}{300 \text{ s}} = 1.6 \text{ meters/second}$

Thus, Gary's average speed is $1.6$ meters per second.

To solve this problem, we'll follow these steps:

• Step 1: Calculate the distance for each part of the journey.
• Step 2: Find the total distance traveled.
• Step 3: Convert all time to hours and include the break time.
• Step 4: Calculate the average speed using the formula for average speed.

Let's calculate each step:

Step 1: Calculate the distances:
For the first part of the journey:
Speed = 82 km/h, Time = 4 hours
Distance = Speed × Time = $82 \times 4 = 328$ km

For the second part of the journey:
Speed = 70 km/h, Time = 3 hours
Distance = Speed × Time = $70 \times 3 = 210$ km

Step 2: Total distance traveled:
Total Distance = Distance of first part + Distance of second part
Total Distance = $328 + 210 = 538$ km

Step 3: Calculate total time including the break:
Total time driving = 4 hours (first part) + 3 hours (second part) = 7 hours

Break time = 20 minutes = $\frac{20}{60} = \frac{1}{3}$ hours

Total time = Driving time + Break time = $7 + \frac{1}{3} = \frac{22}{3}$ hours

Step 4: Calculate the average speed:
Average speed $v_{avg} = \frac{\text{Total distance}}{\text{Total time}}$
Average speed $v_{avg} = \frac{538}{\frac{22}{3}} = 538 \times \frac{3}{22} = \frac{538 \times 3}{22} = \frac{1614}{22}$

Simplifying $\frac{1614}{22}$: Average speed ≈ $73.36$ km/h

Therefore, the average speed of George's truck for the entire journey, including the break, is $73.36$ km/h.