- A car left Point A at 7:30 am and arrived at Point B, 162 miles away at 10:30 am. What was its average speed in miles per hour?
- If you lift the same weight through the same distance 9 times, how much work is accomplished?
The correct answer and explanation is:
- Average Speed:
To calculate the average speed, use the formula: Average Speed=Total DistanceTotal Time\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
- Total Distance = 162 miles
- Total Time = 10:30 am – 7:30 am = 3 hours
Now, we can substitute these values into the formula: Average Speed=162 miles3 hours=54 miles per hour\text{Average Speed} = \frac{162 \, \text{miles}}{3 \, \text{hours}} = 54 \, \text{miles per hour}
So, the car’s average speed is 54 miles per hour.
- Work Accomplished:
Work is calculated using the formula: Work=Force×Distance×cos(θ)\text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta)
Where:
- Force is the force applied (usually in newtons),
- Distance is the distance over which the force is applied (in meters),
- θ\theta is the angle between the direction of the force and the direction of the displacement (for vertical lifting, θ=0∘\theta = 0^\circ, so cos(0∘)=1\cos(0^\circ) = 1).
If you lift the same weight through the same distance 9 times, the work accomplished is the total amount of work done for all 9 lifts.
Let’s say the weight you are lifting has a force equivalent to FF newtons, and the distance moved vertically is dd meters.
- The work done for one lift would be W=F×dW = F \times d.
- For 9 lifts, the total work done would be:
Total Work=9×(F×d)=9F×d\text{Total Work} = 9 \times (F \times d) = 9F \times d
In terms of energy, work is measured in joules (J). Thus, if we know the values of FF and dd, we could calculate the exact work. However, the key takeaway is that if you lift the same weight through the same distance 9 times, you are multiplying the work done for one lift by 9, resulting in 9 times the amount of work done in a single lift.
If FF and dd were provided, a specific numerical answer could be computed. But without the exact force or distance, the general formula is 9×work per lift9 \times \text{work per lift}.