An object moving at a constant velocity travels 274 m in 23 s. what is its velocity?

The question Ellen is likely exploring is "In what way does distance influence the gravitational force acting on objects?"

Explanation:

Response:

0.60 m/s

Details:

The average speed between times t = a and t = b can be expressed as:

v_avg = (x(b) − x(a)) / (b − a)

Given the function x(t) = 0.36t² − 1.20t, and considering the interval from 1.0 to 4.0:

v_avg = (x(4.0) − x(1.0)) / (4.0 − 1.0)

v_avg = [(0.36(4.0)² − 1.20(4.0)) − (0.36(1.0)² − 1.20(1.0))] / 3.0

v_avg = [(5.76 − 4.8) − (0.36 − 1.20)] / 3.0

v_avg = [0.96 − (-0.84)] / 3.0

v_avg = 0.60

The average speed calculated is 0.60 m/s.

Response:

83%

Clarification:

At the surface, the weight can be expressed as:

W = GMm / R²

where G denotes the gravitational constant, M represents the Earth's mass, m signifies the shuttle's mass, and R is the Earth's radius.

When in orbit, the weight is given by:

w = GMm / (R+h)²

where h indicates the shuttle's altitude above Earth's surface.

The weight ratio is as follows:

w/W = R² / (R+h)²

w/W = (R / (R+h))²

For R = 6.4×10⁶ m and h = 6.3×10⁵ m:

w/W = (6.4×10⁶ / 7.03×10⁶)²

w/W = 0.83

Thus, the shuttle maintains 83% of its weight as it orbits.

The elevator's acceleration is 0.422 m/s². To clarify the solution: By applying Newton's Law, the net forces in the motion's direction equal the mass multiplied by the acceleration. The forces comprise 460 N in the motion's direction and the person's weight acting in the opposite direction... The weight is determined by the mass and gravity's acceleration (W = mg). Here m = 45 kg and g = 9.8 m/s², leading to W = 441 N. With the scale indicating 460 N, we apply F - W = ma, yielding 19 = 45 a. Dividing both sides by 45 gives a = 0.422 m/s².

Answer:

Explanation:

Transformation of Energy

Also known as energy conversion, this refers to the process in which energy shifts from one type to another. In this context, three energy forms are involved. When the object is stationary at the ramp's peak, it possesses gravitational potential energy, calculated as

As the object descends the frictionless ramp, it converts all its potential energy into kinetic energy, represented as

Thus,

Ultimately, when the object encounters a rough surface, all energy converts to thermal energy. The work performed by the friction force corresponds to the alteration in kinetic energy, as all velocity is lost in this process:

Given the kinetic energy equals the initial potential energy:

The negative sign indicates that the work acted against the direction of movement, meaning the force and displacement are 180° apart.

This outcome is independent of the distance D needed to halt the block or the kinetic friction coefficient.