1) The average velocity is 
2) The instantaneous velocity is 
Explanation:
1)
The average velocity of an object is given by
where
d is the displacement
t is the time elapsed
In this problem, the position of the particle is given by the function
where t is the time.
The position of the particle at time t = 6 sec is
While the position at time t = 12 sec is
So, the displacement is
And therefore the average velocity is
2)
The instantaneous velocity of a particle is given by the derivative of the position vector.
The position vector is
By differentiating with respect to t, we find the velocity vector:
Therefore, the instantaaneous velocity at any time t can be found by substituting the value of t in this expression.
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Answer: 60mph
Explanation:
Given the following :
First leg travel:
Distance = 30 miles
Time of travel= 30 minutes = 0.5 hour
Second leg travel:
Distance = 60 miles
Time of travel = one hour
Average speed :
Speed = total Distance / time of travel
Total distance in miles = (30 + 60) miles = 90 miles
Total time of travel = 1 hour + 0.5 hour = 1.5 hours
Average speed = total distance traveled / total travel time
Average speed = 90 miles / 1.5 hours
Average speed = 60 miles / hour
= 60mph
It has a 10 electrons. Since it's atomic number is 11 it must have 11 protons. Also, given that it has a +1 charge, it has one less electron than protons since they have equal but opposite charges.
The number of protons is the mass number minus the atomic number = 23-11= 12 neutrons.
Answer:
The inside Pressure of the tank is 
Solution:
As per the question:
Volume of tank, 
The capacity of tank, 
Temperature, T' = 
= 299.8 K
Temperature, T = 
= 288.2 K
Now, from the eqn:
PV = nRT (1)
Volume of the gas in the container is constant.
V = V'
Similarly,
P'V' = n'RT' (2)
Also,
The amount of gas is double of the first case in the cylinder then:
n' = 2n
![\]frac{n'}{n} = 2](https://tex.z-dn.net/?f=%5C%5Dfrac%7Bn%27%7D%7Bn%7D%20%3D%202)
where
n and n' are the no. of moles
Now, from eqn (1) and (2):
Answer:
D = 25 miles
Explanation:
To solve this problem, we just need to know how much time it took both bicyclists to collide and that will be the same amount of time that the bee flew at 25miles per hour. With those values we could calculate the distance it traveled.
Since both bicyclists collide, we know that Xa=Xb, so:
Xa = V*t = 10*t and Xb = 20 - V*t = 20 - 10*t
10*t = 20 - 10*t Solving for t:
t = 1 hour Now we can calculate the distance for the bee:
D = Vbee * t = 25 * 1 = 25 miles
