Carolyn B. answered • 06/28/21
Chemistry, Physics, and Biology Tutoring
First let's write down what the problem gives us. The problem says that "the truck's speed increases uniformly from 36 kilometers per hour to 108 kilometers per hour". The truck's initial speed/velocity is 36 kilometers per hour. The symbol for initial speed/velocity is v0. So v0 = 36 kilometers per hour. The final speed of the truck is 108 kilometers per hour. The symbol for final speed/velocity is vf. So vf = 108 kilometers per hour. Finally, the problem says that this increase in speed takes 20 seconds. The symbol for time is t. So t = 20 seconds.
The equation for average speed is Average speed = d / t
In order to calculate the average speed, we need to find the d (displacement). Displacement is another word for "how far did the car move". For this problem, you can think of displacement as the same thing as distance. So first we need to find d.
We need to use the equation d = 0.5 * (v0 + vf) * t to find d. However, since v0 and vf are in kilometers per hour, we need the time (t) to be in hours. Right now the time is in seconds. Since t = 20 seconds and there are 3600 seconds in one hour, we calculate 20 / 3600 to change t into hours.
20 / 3600 = 0.0055555 hour. So we will use t = 0.0055555 hour .
We put the information we have found above into the equation d = 0.5 *(v0 + vf ) * t like this:
d = 0.5 * (36 + 108) *0.055555
First we deal with the 36 + 108. 36 + 108 = 144, so we can replace the 36 + 108 with 144 in the equation:
d = 0.5 * 144 * 0.0055555
Now we just multiply 0.5 * 144 * 0.005555. The calculator says that 0.5*144*0.0055555 = 0.4. Remember that since the initial and final speeds were in kilometers per hour, the distance will be in kilometers. So, the distance covered in 20 seconds is 0.4 kilometers. To convert this distance to meters, remember that 1 km = 1000 meters. So 0.4 x 1000 = 400 meters. So the distance covered can also be expressed as 400 meters.
Average speed is generally expressed in meters/second, so we should use d = 400 meters. We also know from the problem that t = 20 seconds. Now we we use the equation Average speed = d / t . When we put the information in, our equation is:
Average speed = 400 / 20
The calculator says that 400 / 20 = 20. So the average speed is 20 meters per second.
Now we need to find the acceleration. The symbol for acceleration is a. There are several equations we could use, but let's use the equation vf = v0 + a * t . Once again, we will have to use t = 0.0055555 hour . We put the information into the equation like this:
108 = 36 + a * 0.055555
We subtract 36 from both sides:
108 -- 36 = a * 0.0055555
The calculator says that 108 -- 36 = 72, so we replace the 108 -- 36 with 72 in the equation like this:
72 = a * 0.005555
We divide both sides by 0.005555 to get a by itself.
a = 72 / 0.0055555
The calculator says that 72 / 0.0055555 = 12,960.1296 . So a = 12,960.1296 .The units so far for are kilometers/(hour)2 . The problem wants the answer in meter/(second)2. First let's deal with converting the kilometers to meters. We know that 1 km = 1000 m. So we multiply 12,960.1296 by 1000 to change the km to m. 12,960.1296 x 1000 = 12,960,129.6. So a = 12,960,129.6 meters/(hour)2. Now we convert the (hour)2 on the bottom to (seconds)2. We know that 1 hour = 3,600 seconds. So (1 hour)2 = (3,600 seconds)2.
Thus, 1 hour2 = 12,960,000 seconds2. So to convert the hour2 to seconds2, we must divide 12,960,129.6 by 12,960,000 seconds2. 12,960,129.6 / 12,960,000 = 1.000. So a = 1.00 meters/s2
