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?
Let's break down the questions one by one.
1. Calculate the total distance traveled by the car:
To calculate the total distance traveled by the car, we need to find the sum of the distances covered at different speeds.
Distance traveled at 55 mph:
Speed = 55 mph, Time = 80 miles / 55 mph = 1.45 hours
Distance = Speed * Time = 55 mph * 1.45 hours = 79.75 miles (approximately)
Distance traveled at 15 mph:
Speed = 15 mph, Time = 5 miles / 15 mph = 0.33 hours
Distance = Speed * Time = 15 mph * 0.33 hours = 4.95 miles (approximately)
Total distance traveled = Distance at 55 mph + Distance at 15 mph
= 79.75 miles + 4.95 miles = 84.7 miles (approximately)
Therefore, the car travels a total distance of approximately 84.7 miles.
2. a) Calculate the two instantaneous speeds of the horse:
Instantaneous speed is the speed at a particular instant. To calculate it, we need to divide the distance traveled by the time taken for each segment.
For the first segment (to the left):
Distance = 19m
Time = 8.6s
Instantaneous speed = Distance / Time = 19m / 8.6s = 2.21 m/s (approximately)
For the second segment (to the right):
Distance = 12m
Time = 18.4s
Instantaneous speed = Distance / Time = 12m / 18.4s = 0.65 m/s (approximately)
Therefore, the horse's two instantaneous speeds are approximately 2.21 m/s to the left and 0.65 m/s to the right.
b) Calculate the two instantaneous velocities of the horse:
Instantaneous velocity is the velocity at a particular instant and includes the direction.
Since velocity is a vector quantity, we need to consider both the magnitude (speed) and direction for each segment.
For the first segment (to the left):
Velocity = -2.21 m/s (since it's moving to the left)
For the second segment (to the right):
Velocity = +0.65 m/s (since it's moving to the right)
Therefore, the horse's two instantaneous velocities are -2.21 m/s to the left and +0.65 m/s to the right.
c) Calculate the average speed of the horse:
Average speed is the total distance traveled divided by the total time taken.
Total distance traveled = Distance to the left + Distance to the right = 19m + 12m = 31m
Total time taken = Time to the left + Time to the right = 8.6s + 18.4s = 27s
Average speed = Total distance traveled / Total time taken = 31m / 27s = 1.15 m/s (approximately)
Therefore, the horse's average speed is approximately 1.15 m/s.
d) Calculate the average velocity of the horse:
Average velocity is the total displacement (change in position) divided by the total time taken.
Total displacement = Displacement to the left + Displacement to the right = -19m + 12m = -7m
Average velocity = Total displacement / Total time taken = -7m / 27s ≈ -0.26 m/s
Therefore, the horse's average velocity is approximately -0.26 m/s.
1. To solve this problem, we can break it down into two parts: the distance traveled at 55 mi/h and the distance traveled at 15 mi/h.
a) Distance traveled at 55 mi/h:
Distance = Speed x Time
Distance = 55 mi/h x Time
80 mi = 55 mi/h x Time
Time = 80 mi / 55 mi/h
Time = 1.45 hours
b) Distance traveled at 15 mi/h:
Distance = Speed x Time
Distance = 15 mi/h x Time
5 mi = 15 mi/h x Time
Time = 5 mi / 15 mi/h
Time = 0.33 hours
2. To solve this problem, we'll determine the instantaneous speed and velocity for each part of the horse's motion.
a) Instantaneous speed:
Instantaneous speed is the magnitude of the instantaneous velocity. It can be found using the formula:
Instantaneous speed = Distance / Time
For the first part of the motion:
Distance = 19 m
Time = 8.6 s
Instantaneous speed = 19 m / 8.6 s
Instantaneous speed ≈ 2.2093 m/s (rounded to four decimal places)
For the second part of the motion:
Distance = 12 m
Time = 18.4 s
Instantaneous speed = 12 m / 18.4 s
Instantaneous speed ≈ 0.6522 m/s (rounded to four decimal places)
b) Instantaneous velocity:
Instantaneous velocity includes both the magnitude and direction of motion. It can be determined by dividing the distance traveled by the time taken and including the direction as a vector.
For the first part of the motion:
Distance = 19 m
Time = 8.6 s
Direction = left (negative x-axis)
Instantaneous velocity = Distance / Time = -19 m / 8.6 s ≈ -2.2093 m/s (rounded to four decimal places)
For the second part of the motion:
Distance = 12 m
Time = 18.4 s
Direction = right (positive x-axis)
Instantaneous velocity = Distance / Time = 12 m / 18.4 s ≈ 0.6522 m/s (rounded to four decimal places)
c) Average speed:
Average speed is defined as the total distance traveled divided by the total time taken.
Average speed = (Total Distance) / (Total Time)
Total Distance = 19 m + 12 m = 31 m
Total Time = 8.6 s + 18.4 s = 27 s
Average speed = 31 m / 27 s ≈ 1.1481 m/s (rounded to four decimal places)
d) Average velocity:
Average velocity is defined as the total displacement (change in position) divided by the total time taken.
Average velocity = (Total Displacement) / (Total Time)
Total Displacement = 19 m to the left - 12 m to the right = 19 m - 12 m = 7 m (to the left)
Total Time = 8.6 s + 18.4 s = 27 s
Average velocity = 7 m / 27 s ≈ 0.2593 m/s (rounded to four decimal places)