Physics, 11.11.2020 17:50, rowdycar313p0ao5k

A 4.00-kg particle moves along the x axis. Its position varies with time according to x= 5t +1 2.0t^3, where x is in meters and t is in seconds. Find: a. the kinetic energy of the particle at any time t.
b. the acceleration of the particle and the force acting on it at time t.
c. the power being delivered to the particle at time t.
d. the work done on the particle in the interval t = 0 to t =5

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answered: letsgetcookingblog

a) The kinetic energy of the particle at any time t is $K = 50+120\cdot t^{2}+72\cdot t^{4}$ .

b) The acceleration of the particle at time t is $a= 12\cdot t$ . The force acting on the particle at time t is $F = 48\cdot t$ .

c) The power being delivered to the particle at time t is $\dot W = 240\cdot t +288\cdot t^{3}$ .

d) The work done on the particle in the interval t = 0 to t = 5 is 48000 joules.

Explanation:

a) The kinetic energy of the particle is entirely translational, whose formula is:

$K = \frac{1}{2}\cdot m \cdot v^{2}$ (1)

Where:

- Translational kinetic energy, measured in joules.

- Mass of the particle, measured in kilograms.

- Velocity of the particle, measured in meters per second.

The velocity of the particle is the rate of change of the position of the particle in time, that is:

$v = 5+6\cdot t^{2}$ (2)

Where is the time, measured in seconds.

By substituting on (1), we have the following expression: ( $m = 4\,kg$ )

$K = 2\cdot (5+6\cdot t^{2})^{2}$

$K = 2\cdot (25+60\cdot t^{2} +36\cdot t^{4})$

$K = 50+120\cdot t^{2}+72\cdot t^{4}$

The kinetic energy of the particle at any time t is $K = 50+120\cdot t^{2}+72\cdot t^{4}$ .

b) The acceleration of the particle is the rate of change of the velocity of the particle in time, that is:

$a= 12\cdot t$ (3)

Where is the acceleration of the particle, measured in meters per square second.

The acceleration of the particle at time t is $a= 12\cdot t$ .

The force is obtained by multiplying (3) by the mass of the particle. That is to say: ( $m = 4\,kg$ )

$F = m\cdot a$ (4)

$F = 48\cdot t$

The force acting on the particle at time t is $F = 48\cdot t$ .

c) According to the Work-Energy Theorem, the change in kinetic energy of the particle equals the change in the net work done on the particle. In this case, the power is equal to the rate of change in kinetic energy.

$\dot W = \dot K$ (5)

$\dot W = \frac{d}{dt}(50+120\cdot t^{2}+72\cdot t^{4})$

$\dot W = 240\cdot t +288\cdot t^{3}$

The power being delivered to the particle at time t is $\dot W = 240\cdot t +288\cdot t^{3}$ .

d) The work done on the particle (), measured in joules, is equal to the change of the kinetic energy of the particle:

W = K(5)-K(0) (6)

$W = [50+120\cdot (5)^{2}+72\cdot (5)^{4}]-[50+120\cdot (0)^{2}+72\cdot (0)^{4}]$

$W = 48000\,J$

The work done on the particle in the interval t = 0 to t = 5 is 48000 joules.

answered: Guest

two charges are fixed in place on the x-axis as shown. the charge at x = 0 is negative and has magnitude q = 2 μcoulombs (1 μcoulomb = 10-6 coulombs). the charge at x = d, (d = +12 cm), is positive and has magnitude q = 4 μcoulombs. find a point x = xo along the x-axis at which the electric field is zero.

answered: Guest

this is an example of "committed" time.

committed time, as contracted time, takes need over essential and available time since it is seen as profitable work. it alludes to the time allotted to keep up a home and family. at the point when a man is commuting using committed time this individual may feel that the drive is an obligation to family, for example, strolling youngsters to class or driving a mate to work. contracted and committed time clients may feel that their commute could really compare to the commute of important or leisure time clients on the grounds that their commute is profitable work. in this manner, they might be more disposed to pick a mechanized method of movement.

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A 4.00-kg particle moves along the x axis. Its position varies with time according to x= 5t +1 2.0t^...