Solve Kinematic Problems with Graphs?

[anthonybommarito1]

so this is just a general question but is it possible to solve all one dimensional motion problems by making graphs, i feel like if that's the case I wouldn't need to use the kinematic equations. I usually get caught up on problems where acceleration changes over time and I have to do calculations relative to a certain interval of time, but if I was able to just graph the problems I feel like I could be able to find what I needed by taking slopes and areas under curves? So my question is would I be able to solve kinematic word problems just by constructing graphs of the things I was given in the problem?!

 

[berkeman]

so this is just a general question but is it possible to solve all one dimensional motion problems by making graphs, i feel like if that's the case I wouldn't need to use the kinematic equations. I usually get caught up on problems where acceleration changes over time and I have to do calculations relative to a certain interval of time, but if I was able to just graph the problems I feel like I could be able to find what I needed by taking slopes and areas under curves? So my question is would I be able to solve kinematic word problems just by constructing graphs of the things I was given in the problem?!

How are you going to solve for the area under a curve? There's a way to do it using your proposal, but it's not pretty...

 

[anthonybommarito1]

How are you going to solve for the area under a curve? There's a way to do it using your proposal, but it's not pretty...

Well I could try to get some function of t using my initial conditions and integrate it... But I'm honestly not too sure... I was just making up example problems to test solving by graphing and it didn't work out as easily as I thought or wished it had :(

 

[berkeman]

problems where acceleration changes over time

When acceleration changes over time, you would generally need to use integral calculus to solve the problems, IMO.

 

[anthonybommarito1]

When acceleration changes over time, you would generally need to use integral calculus to solve the problems, IMO.

Quick question what would I do if something acceleration is changing oVer time, like in a certain interval it's 3m/s^2 then for 6 seconds it's zero and then the next x about of seconds it's a negative value... How would I go about finding like a total velocity... Questions of this manner make me thinking using the graph method is the best because you arnt given a function of t to integrate as you would in a calc course... Could I like derive an acceleration function to integrate?

 

[haruspex]

Quick question what would I do if something acceleration is changing oVer time, like in a certain interval it's 3m/s^2 then for 6 seconds it's zero and then the next x about of seconds it's a negative value... How would I go about finding like a total velocity... Questions of this manner make me thinking using the graph method is the best because you arnt given a function of t to integrate as you would in a calc course... Could I like derive an acceleration function to integrate?

To have any hope of getting an answer you must be told how acceleration varies as a function of time. It need not be one simple equation, but enough information that you can determine what the acceleration is at each instant.
If the acceleration is a step function or linear on each of the time intervals then you can get the answer by graphing. But you can also get the answer by writing an integral for each such interval. And if the function of time is anything more complicated over some intervals then you will have to use integration for those.