Acceleration as a Function of Velocity

In summary, the problem involves finding the acceleration (a) at a given time (t=3s) when the velocity (v) is known to be 6 ft/sec at t=2s, and the equation a=4/v is used to solve for a. The units for acceleration are in ft/sec^2 and the constant 4 has no units.
  • #1
DeboPGH
3
0

Homework Statement



When 2<=t<=6
v= 4/a in ft/sec2

v= 6 ft/sec @ t=2s

Find a at t=3s


Homework Equations



a=dv/dt.

The Attempt at a Solution



My integration is horribly wrong and honestly not worth typing. LOL
 
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  • #2
DeboPGH said:

Homework Statement



When 2<=t<=6
v= 4/a in ft/sec2

v= 6 ft/sec @ t=2s

Find a at t=3s


Homework Equations



a=dv/dt.

The Attempt at a Solution



My integration is horribly wrong and honestly not worth typing. LOL

You write,

v= 4/a in ft/sec^2

something is goofy here, something is not right?
 
  • #3
Spinnor said:
You write,

v= 4/a in ft/sec^2

something is goofy here, something is not right?

I'm sorry...acceleration (a) should be in ft/sec^2

so a=4v^-1
 
  • #4
Now you have acceleration = 4/velocity what are the units of the 4

acceleration * time has units of velocity. Your expression a=4v^-1 still confuses me. Does the number 4 have units? I'm missing something that others might be missing as well.
 
  • #5
Spinnor said:
Now you have acceleration = 4/velocity what are the units of the 4

acceleration * time has units of velocity. Your expression a=4v^-1 still confuses me. Does the number 4 have units? I'm missing something that others might be missing as well.

No units on 4 it's just a constant?

the original problem is v = 4 divided by acceleration or v = 4/a

I solved for acceleration (a hint by my professor) so acceleration = 4 divided by velocity or a = 4/v
 

What is acceleration?

Acceleration is the rate of change of velocity over time. It is a measure of how quickly the velocity of an object is changing.

How is acceleration calculated?

Acceleration is calculated by dividing the change in velocity by the change in time. This can be represented by the formula a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

What is the difference between acceleration and velocity?

Velocity is a vector quantity that describes the speed and direction of an object, while acceleration is the rate of change of velocity. In other words, velocity tells us how fast an object is moving and in what direction, while acceleration tells us how quickly the velocity is changing.

How does acceleration affect an object's motion?

Acceleration affects an object's motion by changing its velocity. If an object has a positive acceleration, it will speed up, while a negative acceleration will cause it to slow down. The direction of the acceleration will also affect the direction of the object's motion.

What are some examples of acceleration as a function of velocity?

One example is a car accelerating from a stop sign. The velocity of the car increases as it accelerates. Another example is a ball thrown into the air. The velocity of the ball decreases as it reaches its highest point, representing a negative acceleration due to gravity.

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