When simple motion begins is there acceleration and jerk

[spikehoward]

Ive been looking at the simple physics problems for 2D motion. For example, a ball starts from rest and is thrown at 5m/s at an angle of 30 degrees with respect to the ground on earth. Most of the problems assume that the acceleration in the x-direction is 0. Doesnt there need to be an initial acceleration to get from rest to a constant velocity? Can we just ignore that instant for calculations?

In general when motion starts, is there always an increase in acceleration, jerk, onto the umpteenth derivative?

 

[Drakkith]

Doesnt there need to be an initial acceleration to get from rest to a constant velocity? Can we just ignore that instant for calculations?

Yes, the problems are ignoring any acceleration to keep things simple.

In general when motion starts, is there always an increase in acceleration, jerk, onto the umpteenth derivative?

That's right.

 

[hilbert2]

In general when motion starts, is there always an increase in acceleration, jerk, onto the umpteenth derivative?

If we have an object at rest until time ##t=t_0## and at that moment it instantly accelerates to velocity ##v##, it's said that the acceleration ##a(t_0 )## is infinite and ##a(t) = v\delta (t-t_0 )##. Here ##\delta (t)## is a Dirac delta distribution - something that's nonzero at only one point but still has a nonzero integral. In the sense how derivatives are calculated for distributions, it does have nonzero derivatives of arbitrarily high order.

 

[Nidum]

When a ball is said to be launched with a constant velocity this can be unambiguously true physically . The acceleration of the ball takes place while it is still being held by the thrower . The instant it loses contact with the throwers hand the ball undergoes no further acceleration and therefore it is launched at a constant velocity .

The action is generally smooth and there is certainly no step change in the ball's velocity at any point in the throw .

There are many other examples of this type of action where a body is accelerated by a mechanism and then has constant velocity after release .

 

[sophiecentaur]

Doesnt there need to be an initial acceleration to get from rest to a constant velocity? Can we just ignore that instant for calculations?

This is the beauty of the concept of 'Impulse'. Impulse is change of Momentum and the time taken to achieve that change is not relevant. This means that there are many calculations (collisions are a good example) where the actual time of contact / acceleration can be ignored; all that matters are the before and after situations and we know that Momentum of the whole system is not changed (conserved).