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horrorfan [7]
3 years ago
7

The motion of a particle along a straight line is described by the equation x=6+4t2 -t 4 , where x is in meter and t is in secon

ds. Find position, velocity, and acceleration of the object when t=2s.
Physics
1 answer:
Aleks [24]3 years ago
5 0

Answer:

The position of the particle is 6m

The velocity of the particle is 16 m/s in negative direction

The acceleration of the object is -40 m/s²

Explanation:

Given;

motion of the particle along a straight line as x = 6 + 4t² - t⁴

The position of the object when t = 2s

x = 6 + 4(2)² - (2)⁴

x = 6 + 16 - 16

x = 6m

The velocity of the object when t = 2s

Velocity = dx/dt

dx/dt = 8t - 4t³

when t = 2s

Velocity = 8(2) - 4(2)³

Velocity = 16 - 32

Velocity = -16m/s

Velocity = 16 m/s (in negative direction)

The acceleration of the object when t = 2s

Acceleration = d²x/dt² = 8 - 12t²

Acceleration = 8 - 12 (2)²

Acceleration =  -40 m/s²

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Explanation:

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3 years ago
) A stone initially moving at 8.0 m/s on a level surface comes to rest due to friction after it travels 11 m. What is the coeffi
natali 33 [55]

Answer:

-0.3

Explanation:

F' = μmg ........... Equation 1

Where F' = Frictional force, μ = coefficient of kinetic friction, m = mass of the stone, g = acceleration due to gravity.

But,

F' = ma ............ Equation 2

Where a = acceleration of the stone.

Substitute equation 2 into equation 1

ma = μmg

dividing both side of the equation by m

a = μg

make μ the subject of the equation

μ = a/g............... Equation 3

From the equation of motion,

v² = u²+2as................. Equation 4

Where v and u are the final and the initial velocity respectively, s = distance.

Given: v = 0 m/s (to rest), u = 8.0 m/s, s = 11 m.

Substitute into equation 4

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a = -64/22

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Explanation:

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Or, 80% = (4000J/input work) ×100%

Or, 80%/100% = 4000J/inputwork

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