Super easy driving question - instantaneous acceleration

[physicsgurl12]

super easy driving question -- instantaneous acceleration

Homework Statement

a Person in a car is driving down a straight road. The instantaneous acceleration is decreasing with time but is directed in the same direction as the cars motion the speed of the car is constant or increasing with time. explain

The Attempt at a Solution

i know its not decreasing with time.

 

[I like Serena]

Hi again physicsgurl12!

For this you need to understand a little bit about acceleration and speed.

The definition of acceleration is: the change in speed per unit of time.
(Similarly the definition of speed is: the change in position per unit of time.)

So if acceleration is positive, this means that the change in speed is also positive, meaning that speed increases.

Can you tell whether the acceleration is positive or negative?

 

[CheckMate]

If the direction of acceleration is directed in the same direction as the car's velocity than it must be positive.

If the car's acceleration is positive (greater than zero) than the velocity must be increasing per unit time, regardless if the acceleration is decreasing in terms of magnitude.

Example : Velocity starts at 10 m/s forward at t=1
Acceleration is 10 m/s^2 (same direction as velocity) at t=1s forward but decreases to 2 m/s^2 at t=2s. Speed at t=2s (new speed) will be 14 m/s instead of being 20 m/s if the acceleration was constant.

The car is still going forward and it's speed is increasing because you still have an acceleration in the same direction.

 

[physicsgurl12]

negative. because its decreasing?

 

[I like Serena]

negative. because its decreasing?

Consider the speed of a skateboard.
Let's assume that the speed of the skateboard is decreasing.
Does that mean the speed is negative, or in other words that your skateboard is moving backward?

 

[CheckMate]

negative. because its decreasing?

No decreasing means going from a big value to a lesser value. Going from 10 to 3 is decreasing.

Negative means less than zero. A negative acceleration would be an acceleration against the car.

If you drive a car into a building the car will stop and go backwards because the building is doing a negative acceleration relative to the car's initial trajectory.

 

[physicsgurl12]

Consider the speed of a skateboard.
Let's assume that the speed of the skateboard is decreasing.
Does that mean the speed is negative, or in other words that your skateboard is moving backward?

moving backwards? because its distance and if the speed decreases it doesn't mean it has to go behind the orgin.

 

[I like Serena]

moving backwards? because its distance and if the speed decreases it doesn't mean it has to go behind the orgin.

Uhh, right.
So when you're moving forward with a decreasing speed, you're still going forward, meaning you have a positive speed.
That is, until the speed becomes zero, after which you would be going backward.

Now back to the problem.
So your acceleration is decreasing.
Does the problem statement say in which direction the acceleration is (even though it is decreasing)?

 

[physicsgurl12]

Uhh, right.
So when you're moving forward with a decreasing speed, you're still going forward, meaning you have a positive speed.
That is, until the speed becomes zero, after which you would be going backward.

Now back to the problem.
So your acceleration is decreasing.
Does the problem statement say in which direction the acceleration is (even though it is decreasing)?

nope it just its decraseing and opposite of the car.

 

[I like Serena]

nope it just its decraseing and opposite of the car.

Hmm, I read: "The instantaneous acceleration (is decreasing with time but) is directed in the same direction as the cars motion".

 

[physicsgurl12]

oh. just kidding. that's what i get for trying to do two at once

 

[I like Serena]

Sooooooo?

 

[physicsgurl12]

so then its moving the same direction as the car

 

[I like Serena]

Uhh?

What is moving in the same direction as the car?

 

[physicsgurl12]

the acceleration. isn't that what we were talking about?

 

[I like Serena]

Ahhh, well, "acceleration" isn't "moving"...

So the acceleration is in the same direction as the car.
What does that tell you about the speed of the car?

 

[physicsgurl12]

that its accelerating

 

[I like Serena]

Good! :shy:

Do you have the answer to your problem now?

 

[physicsgurl12]

um i feel like its constant because its decreasing acceleration even though its going the same direction as the car

 

[I like Serena]

Uhh... exactly what is constant?

 

[physicsgurl12]

speed?

 

[I like Serena]

Uh, well, we just established that the acceleration was in the direction of the motion of the car.
Since the change in speed (per unit of time) equals the acceleration, the speed cannot be constant...

 

[physicsgurl12]

okay so then the speed is increasing with time.

 

[I like Serena]

Guessing?
Or do you get it now?

But yes, you're right!

 

[physicsgurl12]

no i get it now. thanks.