You are driving home on a weekend from school at 65mph for 130 miles. It then starts to snow and you slow to 45 mph. You arrive home after driving 4 hours. How far is your hometown from school?
First I found the time with d/v=t so 130/65= 2 hours
Then I used d= (v-v_0)/(t-t_0)
=(45-65)/(4-2)
=-20mph/2hours
=-10 miles
distance can't be negative can it so Would the answer just be 10 miles?
Figure the time on each leg (first leg 130mi/65mph, second leg is 4hrs minus first time).
distance = 130mi + timesecondleg*45mph
To find the distance between your hometown and school, we can use the formula d = v * t, where d is the distance, v is the velocity, and t is the time.
First, let's calculate the time it took for you to drive 130 miles at a speed of 65 mph:
t = d / v = 130 miles / 65 mph = 2 hours.
Next, we need to calculate the distance you traveled at a speed of 45 mph for the remaining time. Since you drove for a total of 4 hours and spent 2 hours driving at 65 mph, the remaining time would be 4 - 2 = 2 hours.
Using the formula again:
d = v * t = 45 mph * 2 hours = 90 miles.
Now, to find the total distance traveled, we add the distances covered at each speed:
130 miles + 90 miles = 220 miles.
So, the distance between your hometown and school is 220 miles.
It's important to note that in this scenario, the negative value you encountered occurred because your formula for calculating the distance between two speeds assumes a constant acceleration or deceleration. However, in reality, your speed simply changed from 65 mph to 45 mph, resulting in a distance of 10 miles.