1. A car travels 80 mi at a speed of 55mi/h. It encounters traffic and only travels at a speed of 15mi/h for a distance of 5mi.
2. A horse travels at 19m to left for 8.6s, and then turns around and travels 12m to the right for 18.4s.
a) What are the horse's two instantaneous speeds?
b) What are the horse's two instantaneous velocities?
c) What is the horse's average speed?
d) What is the horse's average velocity?
1. To find the total distance traveled by the car, we need to add the distance traveled at each speed.
Distance traveled at 55 mi/h:
Distance = Speed x Time
Distance = 55 mi/h x (80 mi / 55 mi/h)
Distance = 80 miles
Distance traveled at 15 mi/h:
Distance = Speed x Time
Distance = 15 mi/h x (5 mi / 15 mi/h)
Distance = 5 miles
Total distance traveled by the car = 80 miles + 5 miles = 85 miles.
2. a) To find the horse's two instantaneous speeds, we divide the distance traveled by the time taken at each segment.
For the first segment:
Speed = Distance / Time
Speed = 19 m / 8.6 s
Speed ≈ 2.209 m/s (rounded to three decimal places)
For the second segment:
Speed = Distance / Time
Speed = 12 m / 18.4 s
Speed ≈ 0.652 m/s (rounded to three decimal places)
b) Instantaneous velocity takes into account the direction of travel. Since the horse travels to the left and then turns around and travels to the right, the velocity will be negative for the first segment and positive for the second segment.
For the first segment:
Velocity = -2.209 m/s (negative as the horse is traveling to the left)
For the second segment:
Velocity = 0.652 m/s
c) Average speed is calculated by dividing the total distance traveled by the total time taken.
Distance traveled = 19 m + 12 m = 31 m
Total time taken = 8.6 s + 18.4 s = 27 s
Average speed = Distance traveled / Total time taken
Average speed = 31 m / 27 s
Average speed ≈ 1.148 m/s (rounded to three decimal places)
d) Average velocity takes into account the direction of travel. Since the horse turns around and travels in both directions, the average velocity will be zero because the displacements to the left and right cancel each other out.
Average velocity = 0 m/s
To solve these problems, we need to use a few key formulas and principles of physics. Let's go step by step to find the answers to both problems.
1. Car traveling with varying speeds:
a) To find the total time taken by the car, we need to calculate the time taken for each segment of the journey and add them up. The formula to calculate time is:
Time = Distance / Speed
For the first segment: Time1 = 80 miles / 55 miles per hour
For the second segment: Time2 = 5 miles / 15 miles per hour
Now add the two time segments together to find the total time taken.
b) To find the average speed of the car for the entire journey, we use the formula:
Average Speed = Total Distance / Total Time
The total distance is given as 80 miles + 5 miles (since both segments are in the same direction). Divide this distance by the total time calculated in part (a).
2. Horse traveling with different distances and times:
a) Instantaneous speed is the speed at a specific moment in time. To find this, we take the ratio of the distance covered to the time taken for each segment of the journey.
For the first segment, divide the distance traveled (19m) by the time taken (8.6s).
For the second segment, divide the distance traveled (12m) by the time taken (18.4s).
b) Instantaneous velocity is the speed and direction of an object. To calculate this, we need to know the direction the horse is traveling. If the horse travels towards the left as positive and towards the right as negative, then:
For the first segment, the velocity is positive because it is traveling to the left.
For the second segment, the velocity is negative because it is traveling to the right.
c) Average speed can be calculated by dividing the total distance traveled by the total time taken. In this case, add the distances traveled in both segments and divide by the sum of the time taken for both segments.
d) Average velocity involves both speed and direction. Since the horse starts by going left and then turns around to go right, the net displacement is zero (it ends up where it started). Therefore, the average velocity is also zero.
Now that you know the steps for each problem, you can plug in the given values and solve for each quantity. Let me know if there's anything else I can assist you with!