Solving for Time Change: a=-300v^2

In summary, the conversation is discussing a homework question about finding the time taken for acceleration to change from 1.50ms^-1 to 0.75ms^1 using the equation a=dv/dt. The participants suggest using integration and separation of variables as techniques to solve the problem. One participant clarifies the terminology and suggests integrating both sides of the equation.
  • #1
lycheeliang
2
0

Homework Statement


From eqn a=-300v^2
Find time taken for acceleration to change from 1.50ms^-1 to 0.75ms^1


Homework Equations


a=dv/dt


The Attempt at a Solution



I tried integrating, but still cannot get the ans.
 
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  • #2
This is a simple differential equation. Try separation of variables.
 
  • #3
JohnDuck is quite right, except I think the usual term is 'separable' rather than 'separation of variables'. And it is fairly easy. You'll just have to be clearer to us where you are confused.
 
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  • #4
"separable' is the adjective, "separation" the noun. Yes, this is a "separable" equation and the technique for solving is "separation of variables"- you are both right.

lycheeliang, you have dv/dt= -300v2 so, separating the variables (the verb form!) you have dv/v^2 = -300dt. Integrate both sides of that.
 
  • #5
oh thanks!
 

FAQ: Solving for Time Change: a=-300v^2

What does the equation a=-300v^2 represent?

The equation represents the acceleration of an object in motion, which is dependent on the velocity (v) of the object. The value of -300 is a constant that is used in this specific scenario.

How do you solve for time change in this equation?

To solve for time change, you can use the formula t = v/a, where t represents time, v represents velocity, and a represents acceleration. In this equation, you would substitute -300v^2 for a and solve for t.

What is the unit of measurement for time in this equation?

The unit of measurement for time in this equation will depend on the units used for velocity and acceleration. For example, if velocity is measured in meters per second and acceleration in meters per second squared, then time would be measured in seconds.

How does the value of velocity affect the time change in this equation?

The value of velocity will directly affect the time change in this equation. As the velocity increases, the time change will decrease. This is because the acceleration (a) is multiplied by the square of the velocity (v^2), so a higher velocity will result in a larger value for a and therefore a smaller value for time (t).

Can this equation be used for any type of motion?

No, this equation is specifically used for motion with a constant acceleration of -300v^2. It may not be applicable to other types of motion with different acceleration values. Additionally, this equation assumes that the initial velocity is 0 and there are no external forces acting on the object.

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