## “Does that mean you’re increasing your speed 2.5 meters every second?” Acceleration formula

I saw a comment on a video on Youtube,

About acceleration. A teacher basically said that acceleration is Δv/Δt

He gave a situation where a person went from 5 m/s to 10 m/s and calculated the acceleration, assuming a constant acceleration.

Someone left this comment:

What does 2.5 actually represent?

Does that mean you’re increasing your speed 2.5 meters every second?

And how would this work with a non constant acceleration, since most acceleration isn’t constant?

A car takes longer to go from 60 to 100 than it does to go from 0 to 60. How does m/s^2 actually come into play in the real world?

If it can’t be used for the way cars accelerate then why does it matter?

Here is my response:

It’s written as 2.5 m/s^2, but it may make more sense to think about as being [ 2.5 m/s (units of velocity) per second ]. 2.5(m/s)/s.

That means that the person’s velocity increases by 2.5 m/s each second.

The acceleration is the rate of change of the velocity, how much the velocity changes in a given amount of time. You increase by the units of velocity, m/s, each s.

In a car, a constant acceleration will feel ‘smooth’. So that may be what you want to do as you drive.

Let’s say, you start a car, 0 m/s.

And let’s say you do accelerate at a constant 5 m/s.

You would be going 0 m/s
After 1s, 5 m/s
After 2s 10 m/s
After 3s 15 m/s

The constant acceleration will be more comfortable than a ‘jerky’ acceleration.

If you think about another equation in physics, KE = 1/2 m v^2, you’ll see that higher velocities require more energy. That is related to why you cannot accelerate as quickly from 60 to 100 compared to 0 to 60. (I’m assuming you mean mph or km/hour).

Much of the time in an early level physics classes, at least towards the beginning of the class, you mostly deal with constant accelerations.

It is easier to calculate.

But also, it can be useful, especially when you think about average velocities and average accelerations.

And in another common situation, the acceleration due to gravity is constant for many situations.

You can definitely deal with non-constant acceleration in physics, it involves calculus. I’m not sure what math/physics you are taking currently.

## Physics, Superballs, and the RLC Circuit!

If you bounce a superball it might bounce pretty high on the way up, but it won’t quite make it to the top.

A spring also experiences resistance and in a circuit it is blatantly labeled “resistance.”

Therefore an RLC circuit will experience damped harmonic motion.

An RLC circuit can still be quite useful though, one case in which they are used is in radio receivers.

If the capacitance is adjusted then the natural frequency will change and the amplitude will increase greatly for a certain frequency (similar to how a swing increases distance with a certain frequency).

## LRC Circuit, Differential Equations, and an Easier Approach – Phaser Diagrams

An LRC circuit can be described by a second order differential equation, which in truth would take a long time to solve!

However, we also know that since each part is in series then the current will be the same throughout the circuit.

When we project the A onto the y-axis we get a and this functions like a cosine and/or sine.

We can then use “phaser diagrams” for the process.

There will be three different stages in the circuit and since the currents are lined up then the diagrams can be lined up accordingly and added vectorially.

## Richard Feynman – Science and Chess

Nobel Laureate Richard Feynman compares science to chess. In chess you might also observe a game and thus deduce ‘laws’ or rules.

## How to Simplify Physics Problems

To make physics simpler, an object can be approximated to act like it has all its mass concentrated at a single point.

This single point is called the ‘center of mass’. If the density of the object is uniform, it is simple to compute.

For instance, if a metal rod is of uniform density, the center of mass is just the center of the rod.

Techniques of integration can be used for more complicated situations, but clever analysis of an object can allow you to understand if it is symmetric about an axis or be twice the amount of one side of it.

Observations like these can lessen the work necessary.

## Physics of Freeway Entrances

On round freeway turnouts there are almost always signs that say to slow down to a lower speed.

The reason for this is that the frictional force of the tires on the road will not always be enough to keep a car under control at a higher speed.

Two devices that civil engineers use when constructing roads to make them safer are giving the turnout circle a bigger radius and putting it at an angle.

Making the circle have a bigger radius will make the turn less sharp (thus lowering the centripetal acceleration).

Putting the turnout at an angle will make the normal (perpendicular to the surface) force have a component that keeps the car from losing control.

Both these methods will make it technically safer to drive at higher speeds on such a turnout, but it’s definitely still advisable to slow down.

## Momentum, Baseball Bats, & Superstition

In any given system the total momentum will remain constant.

For the case of Sammy Sosa, a corked bat is lighter and might therefore be swung faster, but momentum is mass multiplied by velocity, so the higher velocity will be cancelled out by a lesser mass.

Also the bat is only in contact with the ball for about 1/1000 second, so the “trampoline” effect of the cork will not be great at all– the time of contact is so short.

The cork center can have a negative effect too, since energy that makes the more springy bat change shape will not be available to propel the ball forward.

The benefits probably are mostly psychological, since many ball players are superstitious.

## Moments of Inertia & Spinning

Different types of moments of inertia can be better suited to different purposes and situations.

If you wanted to store power in a spinning object, you could store more power in an object with a greater moment of inertia since it would be harder to both start and stop the spinning.

However, for something like a bicycle tire you don’t want it to be hard to spin and to stop spinning.  It will be more useful if you just concentrate all the energy into moving forward efficiently.

A disc with more mass toward the center will go faster than a hoop with the mass on the outside.

The disc that is easier to spin wouldn’t be efficient in storing power though.

## Impulse and Momentum

Closely related to momentum is impulse (denoted by J), which is simply the initial momentum subtracted from the final momentum.

The idea of impulse is important in things like mechanical engineering in which objects crash into each other.

The late scientist Harold Edgerton was able to further examine impulse and show how bodies interact when they crash at high speeds by using his strobe light.

Things such as baseballs being hits by bats and bullets going through playing cards could then be analyzed.

Impulse has more important consequences in car safety and the force of impact can be found by knowing the impulse through the equation F=J/Δt.

## Using Conservation of Energy for Motion Problems

In motion problems you can use the truth, but you can also sometimes use the principle of conservation of energy, and it is often simpler.

In a closed system, energy will not be created or destroyed, but it can change forms, ie from potential energy to kinetic energy.

In the carnival game where you try to roll a ball over a hill and up an incline so that it doesn’t return over the hill on the way back, it would be impossible if there were no friction, but since there is friction- it is very difficult to be precise enough.

The energy lost due to friction makes it possible to go over the first incline and still not quite have enough energy to make it back over.

The presence of friction may make a system seem like it loses energy, but the energy in friction becomes heat and is not really “lost”.

When manipulating equations for initial and final energy, it is not really necessary to memorize a negative sign to put in a certain place, but one should know that the initial will always equal the final and the sign, for something like friction, should be changed accordingly.