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2 years ago

Derive equation of motion s=ut+1/2at²

Physics

1 answer:

Pavel [41]2 years ago

4 0

Recall the definitions of

• average velocity:

v[ave] = ∆x/∆t = (x[final] - x[initial])/t

Take the initial position to be the origin, so x[initial] = 0, and we simply write x[final] = s. So

v[ave] = s/t

• average acceleration:

a[ave] = ∆v/∆t = (v[final] - v[initial])/t

Assume acceleration is constant (a[ave] = a). Let v[initial] = u and v[final] = v, so that

a = (v - u)/t

Under constant acceleration, the average velocity is also given by

v[ave] = (v[final] + v[initial])/2 = (v + u)/2

Then

v[ave] = s/t = (v + u)/2 ⇒ s = (v + u) t/2

and

a = (v - u)/t ⇒ v = u + at

so that

s = ((u + at) + u) t/2

s = (2u + at) t/2

s = ut + 1/2 at²

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Gasoline burns in the cylinder of an automobile engine. During the combustion reaction, the production of gas forces the piston

serg [7]

Answer:

$\Delta U = 1640 J$

Explanation:

As we know by first law of thermodynamics that for ideal gas system we have

Heat given = change in internal energy + Work done

so here we will have

Heat given to the system = 2.2 kJ

Q = 2200 J

also we know that work done by the system is given as

$W = 560 J$

so we have

$\Delta U = Q - W$

$\Delta U = 2200 - 560$

$\Delta U = 1640 J$

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3 years ago

Allyson and Adrian have decided to connect their ankles with a bungee cord; one end is tied to each person's ankle. The cord is

Damm [24]

Complete question is;

Allyson and Adrian have decided to connect their ankles with a bungee cord; one end is tied to each person's ankle. The cord is 40 feet long, but can stretch up to 120 feet. They both start from the same location. Allyson moves 10 ft/sec and Adrian moves 9 ft/sec in the directions indicated. Adrian stops moving at time t = 5.5 sec, but Allyson keeps on moving 10 ft/sec in the indicated direction. (If a coordinate system is used, assume that the girls' starting position is located at

(x, y) = (0, 0) and that Allyson and Adrian move in the positive y and negative x directions, respectively. Let one unit equal one foot.)

Compute the length of the bungee cord at t = 7 seconds. (Round your answer to three decimal places.)

Answer:

Length of bungee cord = 85.734 ft

Explanation:

We are told that Adrian moves 9ft/sec. Thus, at 5.5 seconds, distance he moved is; 9 ft/sec × 5.5sec = 49.5 ft in the negative x (-x) direction. Therefore, the coordinate is (-49.5, 0).

Now, Allyson has moved 10ft/sec. Thus, at 7 seconds, distance he moved would be; 10 ft/sec x 7sec = 70 feet in the positive (+y) direction. Therefore, the coordinate is (0, 70).

Now, since they started from the origin, it means (0, 0) is a coordinate. Thus, we now have 3 coordinates which are; (0, 0), (0, 70) & (-49.5,0). These 3 coordinates would therefore combine to form a right triangle.

The hypotenuse is the distance between Allyson and Adrian.

Thus, from pythagoras theorem, we can find the distance between them which is same as the length of the cord.

Thus;

(-49.5)² + 70² = D².

D² = 2450.25 + 4900

D = √7350.25

D = 85.734 ft

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3 years ago

Which statement about dwarf planets is true?

sineoko [7]

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3 years ago

Read 2 more answers

How does the resultant displacement change as the angle between two vectors increases from 90° to 120°?

user100 [1]

The resultant displacement between the two vectors will increase.

The resultant of the two vectors is given by parallelogram law of vectors.

The parallelogram law of vector addition states that if two vectors are represented in magnitude and direction by the adjacent sides of a parallelogram, the diagonal of the parallelogram drawn from the point of intersection of the vectors represents the resultant vector in magnitude and direction.

The resultant of these vectors, say vector A, and B, is given as;

$R^2 = a^2 + b^2 -2ab.Cos (\theta )$

When;

θ = 90°

$R^2 = a^2 + b^2$

When;

θ = 120°

$R^2 = a^2 + b^2 + ab$

Thus, the resultant displacement between the two vectors will increase.

Learn more here: brainly.com/question/20885836

8 0

3 years ago

A thin, rectangular sheet of metal has mass M and sides of length a and b. Find the moment of inertia of this sheet about an axi

Lubov Fominskaja [6]

Answer:

The moment of inertia is $I=\frac{M}{12} a^{2}$

Explanation:

The moment of inertia is equal:

$I=\int\limits^a_b {r^{2} } \, dm$

If r is $-\frac{a}{2}$

and $dm=\frac{M}{a} dr$

$I=\int\limits^a_b {r^{2}\frac{M}{a} } \, dr\\a=\frac{a}{2} \\b=-\frac{a}{2}$

$I=\frac{M}{a} \int\limits^a_b {r^{2} } \, dr\\\\I=\frac{M}{a} (\frac{M}{3} )_{b}^{a}\\ I=\frac{M}{3a} (\frac{a^{3} }{8} +\frac{a^{3} }{8} )\\I=\frac{M}{12} a^{2}$

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4 years ago

Derive equation of motion s=ut+1/2at²​

Derive equation of motion s=ut+1/2at²