The position at time t is
x(t) = 0.5t³ - 3t² + 3t + 2
When the velocity is zero, the derivative of x with respect to t is zero. That is,
x' = 1.5t² - 6t + 3 = 0
or
t² - 4t + 2 = 0
Solve with the quadratic formula.
t = (1/2) [ 4 +/- √(16 - 8)] = 3.4142 or 0.5858 s
When t =0.5858 s, the position is
x = 0.5(0.5858³) - 3(0.5858²) + 3(0.5858) + 2 = 2.828 m
When t=3.4142 s, the position is
x = 0.5(3.4142³) - 3(3.4142²) + 3(3.4142) + 2 = -2.828 m
Reject the negative answer.
Answer:
The velocity is zero when t = 0.586 s, and the distance is 2.83 m
When the acceleration is zero, the second derivative of x with respect to t is zero. That is,
3t - 6 = 0
t = 2
The distance traveled is
x = 0.5(2³) - 3(2²) + 3(2) + 2 = 0
Answer:
When the acceleration is zero, t = 2 s, and the distance traveled is zero.
Answer:
a.
b.
c.
d.
Explanation:
Given:
- angle of inclination of the surface,
- mass of the crate,
- Force applied along the surface,
- distance the crate slides after the application of force,
a.
<u>Work done by the worker who applied the force:</u>
since the direction of force and the displacement are the same.
b.
<u>Work done by the gravitational force:</u>
where:
g = acceleration due to gravity
h = the vertically downward displacement
Now, we find the height:
So, the work done by the gravity:
∵direction of force and displacement are opposite.
c.
The normal reaction force on the crate by the inclined surface:
d.
Total work done on crate is with respect to the worker:
Answer:
C Thy make the force exert all at once
The instantaneous velocity of the object is 36 m/s
The given displacement equation of motion;
To find:
the instantaneous velocity after 5 s;
The instantaneous velocity is the change in displacement per change in time of motion at the given time.
at t = 5 seconds, v = 6(5) + 6 = 36 m/s
Thus, the instantaneous velocity of the object is 36 m/s
Learn more here: brainly.com/question/2234298
Answer:
Energy is transformed from potential to kinetic and vice versa
Explanation:
The energy is transformed from mechanical to kinetic energy when the object changes its position with respect to a reference point, where it loses height but increases its speed. When the object is at maximum height with respect to a reference point, it will have its maximum potential energy value. When the object passes through the reference point it will have potential energy equal to zero, but this energy will become kinetic energy.
The most characteristic and real example is that of a pendulum at one end, as can be seen in the attached image.
When the pendulum is located at the top end, as shown in Figure 1, at that point the maximum potential energy will be held. Then the pendulum is released and when it passes through the reference point and its height is zero, with respect to that point, all potential energy will have become kinetic energy in the same way at this point the maximum speed of the pendulum will be set.