Physics, 25.02.2021 23:10 watervliet2586

Entrance and exit ramps for freeways in (Figure 1) are often circular stretches of road. As you go around one at a constant speed, you will experience a constant acceleration. Suppose you drive through an entrance ramp at a modest speed and your acceleration is 3.0 m/s2 .What will be the acceleration if you triple your speed?

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Answer from: jadenhoughton

27 m/s²

Explanation:

Traveling in uniform circular motion will cause a centripetal acceleration, an acceleration towards the center of the circle.

The acceleration of an object in circular motion is defined as a = v²/r.

Let's set the radius to be 5 m, since it is always unchanging. Solving for the velocity using a = 3 m/s² and r = 3 m gives us:

3 = v²/3 9 = v² 3 = v

The velocity is 3 m/s when the acceleration is 3 m/s² and the radius of the circular path is 3 m.

Now let's triple the velocity: 3 m/s → 9 m/s.

Let's solve for the acceleration using v = 9 m/s and r = 3 m.

a = (9)²/3 a = 81/3 a = 27

The acceleration is 27 m/s² if you triple your speed.

This makes sense because a is directly proportional to v², meaning that if you triple your speed, you increase the acceleration a by a factor of 3², which is a 9 times increase.

a = 3 * 9 = 27 m/s²

As a sidenote, doubling your speed would increase the acceleration by a factor of 2² - a 4 times increase.

Answer from: Quest

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Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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