Answer:
Final velocity of the car will be -9.28 m/sec
Explanation:
We have given that the car starts from the rest so initial velocity of the car u = 0 m /sec
Acceleration of the car in negative direction so acceleration will be
From first equation of motion we know that
v = u+at
So
So final velocity will be -9.28 m/sec
Answer:
a)
b)
Explanation:
Part a
For this case we can begin finding the period like this:
Then we know that the centripetal acceleration is given by:
And the velocity is given by:
If we replace this into the acceleration we got:
And we can replace the values and we got:
Part b
For this case we want to find a value of k such that:
Where a = 9.74, so then we can solve for k like this:
Answer:
A. when the mass has a speed of zero
Explanation:
In mass-spring system, the velocity and the acceleration are in anti-phase, which means that when one of the two quantities is maximum, the other one is zero, and vice-versa.
In fact:
- When the displacement of the spring is zero (x=0), the velocity is maximum, due to conservation of energy. In fact, as the displacement is zero, the elastic potential energy of the system (given by ) is zero, therefore the kinetic energy (given by
) must be maximum, and so the velocity (v) is also maximum. On the cotnrary, acceleration (a) is directly proportional to the restoring force of the spring, given by
so we see that when x=0, then the force is zero: F=0, and so the acceleration is zero as well.
- When the displacement of the spring is maximum, the velocity is zero, due to conservation of energy. In fact, as the displacement is maximum, the elastic potential energy of the system (given by ) is maximum, therefore the kinetic energy (given by
) must be zero, and so the velocity (v) is also zero. On the cotnrary, since acceleration (a) is directly proportional to the restoring force of the spring, given by
so we see that when x=maximum, then the force is maximum, and so the acceleration is maximum as well.
Based on this, the correct answer is
A. when the mass has a speed of zero