Calculating Speed and Energy: Questions on Distance, Power, and Time

[lcg]

I have these questions and I'm not sure which formula to use in each:

This one is confusing as the distances are in miles rather than kilometers:

1. A car is traveling north along a highway and the driver notices that, although the speedometer reads 60mph he actually covers a distance of 5 miles in 5.5 minutes. Calculate the speed of the car.

2. A child can produce a power of 200W. He has to shovel 1000kg of sand from his drive on to the back of a lorry which is at a height of 0.9m above the ground. What is the smallest energy required to shovel the sand?

3. Calculate the shortest possible time that he would need to shovel the sand on to the lorry.

 

[FredGarvin]

1. What is the definition of speed? Isn't it change in distance per unit of time$$S = (\frac{\Delta X}{\Delta t})$$ ?

2. What is the definition of work? Isn't it a force applied over a distance $$W = F* \Delta X$$ ?

3. What is the deinition of power? Isn't it the amount of work per a unit of time $$P = (\frac{W}{\Delta t})$$ ?

For each of these equations, you have to make sure you are using the correct units for your values (e.g. in #1 you will have to convert 5.5 minutes into hours to end up with an answer in miles per hour).

 

[thepatientmental]

1. To calculate the speed of the car, you can use the formula speed = distance / time. In this case, the distance is given in miles and the time is given in minutes. However, it is important to note that the time should be converted to hours for the formula to work. Since there are 60 minutes in an hour, the time of 5.5 minutes should be divided by 60 to get 0.0917 hours. Plugging in the values, we get speed = 5 miles / 0.0917 hours = 54.5 mph. So, the speed of the car is 54.5 mph.

2. To calculate the energy required to shovel the sand, we can use the formula energy = power x time. In this case, the power is given as 200W and the time is not given. However, we can calculate the time by using the formula time = distance / speed. The distance is given as 1000kg and the speed can be assumed to be the same as the speed of walking, which is about 1.4 m/s. So, the time required to shovel the sand would be 1000kg / 1.4 m/s = 714.3 seconds. Plugging in the values, we get energy = 200W x 714.3 seconds = 142,857.1 joules. So, the smallest energy required to shovel the sand would be 142,857.1 joules.

3. To calculate the shortest possible time needed to shovel the sand on to the lorry, we can use the same formula as in question 2, time = distance / speed. In this case, the distance is the same as in question 2, 1000kg, and the speed is given as 1.4 m/s. So, the shortest possible time would be 1000kg / 1.4 m/s = 714.3 seconds. Therefore, the shortest possible time needed to shovel the sand on to the lorry would be 714.3 seconds.

 

[wais]

1. To calculate the speed of the car, we can use the formula speed = distance/time. Since the distance is given in miles and the time in minutes, we need to make sure to convert the units to be consistent. We can convert 5 miles to 8.05 kilometers (since 1 mile = 1.609 kilometers) and 5.5 minutes to 0.0917 hours (since 1 hour = 60 minutes). Now we can plug in the values into the formula: speed = 8.05 km/0.0917 hours = 87.8 km/h. Therefore, the speed of the car is approximately 87.8 km/h.

2. To calculate the energy required to shovel the sand, we can use the formula energy = power x time. The power is given as 200W and the time is not given, so we need to calculate it. We know that the child has to shovel 1000kg of sand, and we can assume that it takes him 1 hour to do so. Now we can plug in the values into the formula: energy = 200W x 1 hour = 200 watt-hours. Therefore, the smallest energy required to shovel the sand is 200 watt-hours.

3. To calculate the shortest possible time to shovel the sand, we can use the formula time = energy/power. The energy is given as 200 watt-hours and the power is given as 200W. Now we can plug in the values into the formula: time = 200 watt-hours/200W = 1 hour. Therefore, the shortest possible time to shovel the sand onto the lorry is 1 hour.