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3 years ago

There is a 3-kg toy cart moving at 4 m/s. Calculate the kinetic energy of the cart.

Physics

1 answer:

m_a_m_a [10]3 years ago

5 0

The kinetic energy of the cart is 24 J.

<u>Explanation:</u>

The acceleration of a given mass from rest to the velocity is known as kinetic energy. It gains energy from acceleration and remains in this state until the speed of the object changes.

The kinetic energy is the given by,

K.E = 1/2 mv^2

Given the mass m = 3 kg, v = 4 m / s.

K.E = 1/2 $\times$ 3 $\times$ (4)^2

K.E = 24 J.

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To stretch a certain nonlinear spring by an amount x requires a force F given by F = 40 x − 6 x 2 , where F is in Newtons and x

strojnjashka [21]

Answer:

64 J

Explanation:

The potential energy change of the spring ∆U = -W where W = work done by force, F.

Now W = ∫F.dx

So, ∆U = - ∫F.dx = - ∫Fdxcos180 (since the spring force and extension are in opposite directions)

∆U = - ∫-Fdx

= ∫F.dx

Since F = 40x - 6x² and x moves from x = 0 to x = 2 m, we integrate thus, ∆U = ∫₀²F.dx

= ∫₀²(40x - 6x²).dx

= ∫₀²(40xdx - 6x²dx)

= ∫₀²(40x²/2 - 6x³/3)

= ∫₀²(20x² - 2x³)

= [20x² - 2x³]₀²

= [(20(2)² - 2(2)³) - (20(0)² - 2(0)³)

= [(20(4) - 2(8)) - (0 - 0))

= [80 - 16 - 0]

= 64 J

5 0

3 years ago

Air is being blown into a spherical balloon at the rate of 1.68 in.3/s. Determine the rate at which the radius of the balloon is

NISA [10]

Answer: 0.006in/s

Explanation:

Let the rate at which air is being blown into a spherical balloon be dV/dt which is 1.68in³/s

Also let the rate at which the radius of the balloon is increasing be dr/dt

Given r = 4.7in and Π = 3.14

Applying the chain rule method

dV/dt = dV/dr × dr/dt

If the volume of the sphere is 4/3Πr³

V = 4/3Πr³

dV/dr = 4Πr²

If r = 4.7in

dV/dr = 4Π(4.7)²

dV/dr = 277.45in²

Therefore;

1.68 = 277.45 × dr/dt

dr/dt = 1.68/277.45

dr/dt = 0.006in/s

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2 years ago

The layer of Earth that we live on

fiasKO [112]

We live on the troposphere

6 0

3 years ago

Pie

Answer:

Explanation:

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3 0

3 years ago

Read 2 more answers

You walk forward at 1.5 m/s for 8s. Your friend decides to walk faster and starts out at 2.0 m/s for the first 4 s. Then she slo

Troyanec [42]

The first thing you should know is that the distance is equal to the speed per time.
Therefore if You walk forward at 1.5 m / s for 8s
d = 1.5t [0,8] s
Your friend decides to walk faster and starts at 2.0 m / s for the first 4 s.
d = 2t [0,4] s
Then she slows down and walks forward at 1.0 m / s for the next 4s
d = t + 4 [4,8] s
Who walked farther?
They both walked the same distance
12 meters

6 0

3 years ago