urgent help please...i need answers for this...
1.) a sprinter accelerates from rest to 10.0 m/s in 1.35 s. what is her acceleration in
a.) in m/s squared
b.) in km/h squared.
2.) a car slows down from a speed of 25.0 m/s to rest 5.00 s. how far did it travel in that time..?
3.) calculate the average speed and average velocity of a complete round-trip in which the outgoing 200 km is covered at
90 km/h,followed by a one-hour lunch break,and the return 200 km is covered at 50 km/h.
4.) a person jogs eight complete laps around a quarter-mile track in a total time of 12.5 min. calculate
a.) it's average speed and
b.) it's average velocity for the entire trip,using "away from the trainer" as the positive direction.
5.) you are driving home from school steadily at 65 mph for 130 miles. it then begins to rain and you slow to 55 mph. you arrive home after
driving 3 hours and 20 minutes.
a.) how far is your hometown from school..?
b.) what was your average speed..?
i'll wait thanks a lot..!!!
Sure, I'll be happy to help you with these questions. Let's address each one step by step.
1.) To find the acceleration of the sprinter, we'll use the formula:
acceleration (a) = change in velocity (Δv) / time taken (Δt)
a.) The sprinter accelerates from rest to 10.0 m/s, so the change in velocity (Δv) is 10.0 m/s. The time taken (Δt) is 1.35 s. Plugging these values into the formula, we get:
acceleration (a) = 10.0 m/s / 1.35 s = 7.41 m/s²
b.) To convert acceleration from meters per second squared (m/s²) to kilometers per hour squared (km/h²), we need to convert the units.
1 kilometer = 1000 meters
1 hour = 3600 seconds
So, to convert m/s² to km/h², we can use the conversion factor of 1 m/s² = (1000/3600) km/h².
Therefore, the acceleration in km/h² is:
7.41 m/s² x (1000/3600) km/h² = 2.053 km/h²
2.) To find the distance the car traveled, we can use the formula:
distance (d) = initial velocity (v₀) x time taken (Δt) + (1/2) x acceleration (a) x (time taken (Δt))^2
In this case, the car slows down from 25.0 m/s to rest, so the final velocity (v) is 0 m/s. The initial velocity (v₀) is 25.0 m/s, and the time taken (Δt) is 5.00 s. Since the car is slowing down, the acceleration (a) is negative.
Plugging these values into the formula, we get:
distance (d) = 25.0 m/s x 5.00 s + (1/2)(-a)(5.00 s)^2
Since the final velocity (v) is 0 m/s, we can simplify the equation to:
distance (d) = 25.0 m/s x 5.00 s
Therefore, the distance traveled by the car is:
distance (d) = 25.0 m/s x 5.00 s = 125 meters
3.) To find the average speed and average velocity of a complete round-trip, we need to consider both the distance traveled and the time taken for each leg of the trip.
The outgoing 200 km is covered at 90 km/h, so the time taken for the first part of the trip is:
time taken (Δt₁) = distance (d₁) / speed (v₁) = 200 km / 90 km/h = 2.22 hours
The return 200 km is covered at 50 km/h, so the time taken for the second part of the trip is:
time taken (Δt₂) = distance (d₂) / speed (v₂) = 200 km / 50 km/h = 4 hours
The total time taken for the round trip is the sum of both legs:
total time taken = Δt₁ + lunch break time + Δt₂ = 2.22 hours + 1 hour + 4 hours = 7.22 hours
The average speed is the total distance traveled divided by the total time taken:
average speed = total distance / total time = (2d) / (Δt₁ + lunch break time + Δt₂) = (2 * 200 km) / 7.22 hours = 55.24 km/h
The average velocity takes direction into account, so we need to consider the displacement. Since it's a round trip, the displacement is 0 km. Thus, the average velocity is also 0 km/h.
4.) To find the average speed and average velocity for the entire trip, we need to consider the distance traveled and the time taken.
a.) The person jogs eight complete laps around a quarter-mile track in a total time of 12.5 minutes. The distance of one lap is a quarter-mile (0.25 miles).
The total distance traveled is:
total distance = (8 laps) x (0.25 miles per lap) = 2 miles
The total time taken is 12.5 minutes which can also be written as 12.5/60 hours:
total time = 12.5 minutes / 60 minutes per hour = 0.2083 hours
The average speed is the total distance traveled divided by the total time taken:
average speed = total distance / total time = 2 miles / 0.2083 hours = 9.595 miles per hour (mph)
b.) The average velocity takes direction into account. In this case, "away from the trainer" is considered as the positive direction. Since the person completes the laps in a circular track, their displacement is zero. Therefore, the average velocity is also zero miles per hour.
5.) Let's address this question step by step:
a.) If you were driving steadily at 65 mph for 3 hours and 20 minutes, we need to convert the minutes to hours. 20 minutes is (20/60) hours or 0.33 hours.
So, the total time taken is:
total time = 3 hours + 0.33 hours = 3.33 hours
To find the distance, we'll use the formula:
distance (d) = speed (v) x time taken (Δt)
Therefore, the distance between your school and hometown is:
distance = 65 mph x 3.33 h = 216.31 miles
b.) The average speed is the total distance traveled divided by the total time taken:
average speed = distance / time = 216.31 miles / 3.33 hours = 64.98 mph
Therefore, the average speed is approximately 64.98 mph.
I hope this helps! Let me know if you have any further questions.