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3 years ago

Slope or velocit ime graph represent

Physics

1 answer:

Lubov Fominskaja [6]3 years ago

7 0

Answer:

Please check the explanation.

Explanation:

The slope of the velocity-time graph illustrates the change in velocity with respect to change in time.

In other words, the acceleration of the object is defined by the slope of a velocity graph. The acceleration can be obtained by finding the slope at a particular time.

Hence, the slope of the velocity time graph represent represents acceleration.

2. Also the acceleration of any object, like a car or bike, at some discrete instant in time 't' is termed as instantaneous acceleration which can be determined if we may take the derivate of the given velocity function.

3. A vector that has a direction and magnitude of 1 is termed as a unit vector, often called a direction vector.

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A uniform thin wire is bent into a quarter-circle of radius a = 20.0 cm, and placed in the first quadrant. Determine the coordin

Mashcka [7]

Answer:

$r_{cm}=[12.73,12.73]cm$

Explanation:

The general equation to calculate the center of mass is:

$r_{cm}=1/M*\int\limits {r} \, dm$

Any differential of mass can be calculated as:

$dm = \lambda*a*d\theta$ Where "a" is the radius of the circle and λ is the linear density of the wire.

The linear density is given by:

$\lambda=M/L=M/(a*\pi/2)=\frac{2M}{a\pi}$

So, the differential of mass is:

$dm = \frac{2M}{a\pi}*a*d\theta$

$dm = \frac{2M}{\pi}*d\theta$

Now we proceed to calculate X and Y coordinates of the center of mass separately:

$X_{cm}=1/M*\int\limits^{\pi/2}_0 {a*cos\theta*2M/\pi} \, d\theta$

$Y_{cm}=1/M*\int\limits^{\pi/2}_0 {a*sin\theta*2M/\pi} \, d\theta$

Solving both integrals, we get:

$X_{cm}=2*a/\pi=12.73cm$

$Y_{cm}=2*a/\pi=12.73cm$

Therefore, the position of the center of mass is:

$r_{cm}=[12.73,12.73]cm$

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