Answer:
a) The average velocity is v = (60 km/h ; 0)
b) The average speed is 60 km/h
Explanation:
The velocity is a vector that has a magnitude and direction. The average speed is the distance traveled over time without taking into account the direction of the motion.
a)The average velocity is calculated as the displacement over time:
v = Δx/Δt
where
v = velocity
Δx = final position - initial position = traveled distance relative to the center of the reference system.
Δt = final time - initial time (initial time is usually = 0)
We know that the displacement is 84 km but we do not know the time. It can be calculated from the two parts of the trip.
In part 1:
v = 45 km/h = 42 km / t
t = 0.93 h
In part 2:
v = 90 km/h = 42 km / t
t = 42 km / 90 km/h
t = 0.47 h
The time of travel is 0.47 h + 0.93 h = 1.4 h
The average velocity will be:
v = 84 km / 1.4 h = 60 km/h
Expressed as a vector in a 2-dimension plane:
v = (60 km/h; 0)
b) The average speed is calculated as the distance traveled over time. Note that in this case, the distance is equal to the displacement since the direction of the motion is always in one direction. But if the direction of the second part of the trip would have been the opposite to the direction of the first part, the displacement would have been 0 (final position - initial position = 0, because final position = initial position), then, the average velocity would have been 0. In change, the average speed would have been the distance traveled (84 km, 42 km in one direction and 42 km in the other) over time.
Then:
average speed = 84 km / 1.4 h = 60 km/h
c) see attached figure.
Answer:
t = 5 s
Explanation:
Data:
Use formula:
Replace:
Solve the subtraction of the numerator:
It divides:
How much time did it take the car to reach this final velocity?
It took a time of <u>5 seconds.</u>
Answer:
Max speed =
Max acceleration =
Explanation:
Given the description of period and amplitude, the SHM could be described by:
and its angular velocity can be calculated doing the derivative:
And therefore, the tangential velocity is calculated by multiplying this expression times the radius of the movement (3 m):
and is given in m/s.
Then the maximum speed is obtained when the cosine function becomes "1", and that gives:
Max speed =
The acceleration is found from the derivative of the velocity expression, and therefore given by:
and the maximum of the function will be obtained when the sine expression becomes "-1", which will render:
Max acceleration =
<u>Answer:</u> The ball is travelling with a speed of 5.5 m/s after hitting the <u>bottle.</u>
<u>Explanation:</u>
To calculate the speed of ball after the collision, we use the equation of law of conservation of momentum, which is given by:
where,
are the mass, initial velocity and final velocity of ball.
are the mass, initial velocity and final velocity of bottle.
We are given:
Putting values in above equation, we get:
Hence, the ball is travelling with a speed of 5.5 m/s after hitting the bottle.