Velocity and acceleration increase

[jshaner858]

Is it possible to have an INCREASING speed AND have the MAGNITUDE of acceleration decreasing?

If so please give examples. I asked my TA this question today and she did not know the answer...? Help!

 

[yourdadonapogostick]

velocity will increase if acceleration is still positive

 

[jshaner858]

yes but is there a situation where you can have increasing speed, but decreasing magnitude of acceleration?

 

[yourdadonapogostick]

yes, as long as a is still positive

 

[jshaner858]

i don't understand...if a is positive and decreasing then you cannot have increasing speed? explain it to me like I'm 4 years old...

 

[yourdadonapogostick]

if you are going 6m/s in the x direction and accelerate int the x direction 2m/s^2 you will speed up, and if you move your acceleration down to 1m/s^2 you will continue speeding up but at a slower rate.

 

[jshaner858]

yes i understand that...but for instantaneous velocity and acceleration it is not possible right? when you accelerate 2 m/ss both speed and accel are increasing, but when you slow down by 1 m/ss then your speed and accel are both decreasing...??

 

[yourdadonapogostick]

nah, you're still increasing

 

[LURCH]

This actually is rocket science! If you are in the Shuttle, and you're burning the engines to go to higher orbit or something, you might do a full-throttle burn for a certain distance, and then back off gradually. So, at first you accelerate with about 4 G's, and later you are only accelerating at about 1 G.

At 4 G's, you might look at your ground-speed indicator and see that, for every second you continue that burn, you go almost 130f/s faster than you were going the previous second. As you throttle back through 2G's, you'll see that you only gain 64f/s for every second you stay at that setting. And when you ease it down to 1G, you'll notice that you're going 32f/s faster for every second you coninue. Yet, even at 1G, you're still accelerating (@32f/s).

So, your magnetude of acceleration has decreased from 4G's through 3 and 2, to 1G, but you were allways accelerating. You just started out accelerating hard, and ended up only accelerating a little.

'Zat make any sense?

 

[Doc Al]

when you accelerate 2 m/ss both speed and accel are increasing,

No. Assuming straight line motion, when your acceleration is 2 m/s^2 it means that your velocity is increasing in the positive direction at a rate of 2 m/s^2. If you are moving in the positive direction, then your speed is increasing. No reason to think your acceleration is changing.

Be careful with directions and signs though. It may be that your speed is actually decreasing, if you were traveling in the negative direction.

but when you slow down by 1 m/ss then your speed and accel are both decreasing...??

Don't say "slow down" when talking about changes to acceleration; slow down refers to changes to speed, which implies an acceleration (not a change in acceleration).

If your acceleration changes from 2 m/s^2 to 1 m/s^2, then you are still speeding up! Just not as quickly. Only when the acceleration goes to zero do you stop accelerating. If it goes negative, then you'll start slowing down.

 

[reilly]

Freshman calculus provides the answer. That is, acceleration is he rate of change of velocity. --true in any frame of reference That's all she wrote.
Regards,
Reilly Atkinson

 

[jshaner858]

Doc Al, I think I understand the way you put it, however, does the word "magnitude" not imply an "absolute value" for acceleration? I have been leaning toward YES as being the answer to my question, but you saying NO has thrown me for a loop.

So the answer is NO, because if you decrease acceleration from 10 to 1, you are still increasing your speed, but your acceleration is decreasing?

 

[krab]

if you decrease acceleration from 10 to 1, you are still increasing your speed, but your acceleration is decreasing?

This is a situation of very common occurrence. Anytime you hit the accelerator in a car, you will accelerate, but because of aerodynamic drag, this acceleration decreases as speed increases.

 

[yourdadonapogostick]

Doc Al, I think I understand the way you put it, however, does the word "magnitude" not imply an "absolute value" for acceleration? I have been leaning toward YES as being the answer to my question, but you saying NO has thrown me for a loop.

So the answer is NO, because if you decrease acceleration from 10 to 1, you are still increasing your speed, but your acceleration is decreasing?

if you mean absolute value as in |\vec{v}|^2=\sum_{j=1}^{n}a_j^2 where n is the number of dimensions of the space in which the vector exists, and a is the coefficient of the unit vector in a given dimenson, then yes, it does have an absolute value. magnitude is always positive. the direction isn't, though. when in one dimension(like your example) it is convenient to use a - sign instead of assigning an angle.

 

[Doc Al]

Doc Al, I think I understand the way you put it, however, does the word "magnitude" not imply an "absolute value" for acceleration?

Not sure what you mean. Magnitude of acceleration is the value of the acceleration regardless of direction or sign.

I have been leaning toward YES as being the answer to my question, but you saying NO has thrown me for a loop.

I'm not sure what question you are referring to. If your question is the one you raised in your first post ["Is it possible to have an INCREASING speed AND have the MAGNITUDE of acceleration decreasing?"], then the answer is a big YES. My point was that (assuming the velocity and acceleration are in the same direction) any acceleration means an increasing speed.

So the answer is NO, because if you decrease acceleration from 10 to 1, you are still increasing your speed, but your acceleration is decreasing?

I'm not sure what question is getting the NO answer, but your statement is completely correct. An acceleration of 10 m/s^2 or 1 m/s^2 both imply an increasing speed. Of course, the greater the acceleration, the greater the rate at which the speed increases.

 

[reilly]

I plead stupid. As long as the accelleration stays positive, velocity can increase -- but at a decreasing rate. If, for example, I go from 32ft/sec/sec to 10ft/sec/sec the speed does continue to increase. My most humble apologies for failing a first year calculus exam.

Regards,
Reilly Atkinson

 

[njmorin]

Whereas velocity the time rate of change of position of a body in a specified direction, acceleration is rate of increase in speed. So regardless of the speed of a body IE: 50 ft per minute, 1000 miles per hour, etc.. that change in velocity to a different value is either acceleration or deceleration (decrease). Acceleration values change depending on the time over which the change in speed occurs. I can increase my speed very slowly (.001g) or very quickly (10g) to get from 10 mph to 20 mph, but in both instances I am accelerating, only at different rates. The difference will be demonstrated in the time it will take to get to the higher speed, but both will cause acceleration to the higher speed.

 

[GRDixon]

Is it possible to have an INCREASING speed AND have the MAGNITUDE of acceleration decreasing?

If so please give examples. I asked my TA this question today and she did not know the answer...? Help!

A mass on a spring. Note that the following is also true (at appropriate times in an oscillation): the speed can be DECREASING while the MAGNITUDE of the acceleration is INCREASING.

 

[njmorin]

Speed is a rate of motion, measured in distance over time. IE: miles per hour.
Acceleration and deceleration are changes in speed, and the rate of those measured in G's. 1G is the rate of acceleration in free fall relative to the force of Earth's gravity(pull force) at sea level. So I can go from 1 to 2 mph at 1g in a certain amount of time at acceleration value x or in twice that time at acceleration value x/2. In both cases my speed is increasing to 2 mph, it just takes twice as long to get to that speed at half the acceleration. Clear as mud? I just did a little presentation for calculating g forces of deceleration for a mine hoist conveyance course I'm teaching. Found some great stuff on wikipedia you might want to go over. 1g acceleration results in 32ft per sec/ per sec btw, and that translates into distance traveled of 32 feet per second squared.

 

[Bob S]

If you are accelerating at constant power, then acceleration is decreasing as velocity is increasing.

P = (d/dt)·(½·m·v²) = constant = m·v·dv/dt = m·v·a

Bob S