# Kinematics of a particle

## Main Question or Discussion Point

Problem: A car starts from rest and moves along a straight line with an acceleration of a=(3s^-1/3)m/sec^2, where s is in metres. Determine the car's acceleration when t=4sec. ANS: 1.06 m/sec^2

Alright...I know nothing about integrals...really, nothing. I was never taught anything about integrals even though I've taken calculus courses before.

Here's what I think I should do.

Take the equation a = d^2s/dt^2 and INTEGRATE it to find the position (s) and substitute it back into the equation. But how do you do this.

## Answers and Replies

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krab
Science Advisor
This is a challenging problem for someone who knows nothing about integration. Anyway, you cannot directly integrate your equation. A trick is to first use

$$a={d^2s\over dt^2}={d\over dt}{ds\over dt}={ds\over dt}{d\over ds}{ds\over dt}=v {dv\over ds}$$

Now you have

$$3s^{-1/3}\,ds=v\,dv$$

which can be integrated. Once you have v as a function of s, you can integrate again to get s as a function of t. Then plug the s at 4 sec. back into the formula for a.

Originally posted by jjiimmyy101
Problem: A car starts from rest and moves along a straight line with an acceleration of a=(3s^-1/3)m/sec^2, where s is in metres. Determine the car's acceleration when t=4sec. ANS: 1.06 m/sec^2

Alright...I know nothing about integrals...really, nothing. I was never taught anything about integrals even though I've taken calculus courses before.

Here's what I think I should do.

Take the equation a = d^2s/dt^2 and INTEGRATE it to find the position (s) and substitute it back into the equation. But how do you do this.
In how many forums u have posted this Que it is already in Maths And Homework Section And in fact Krab and everyone(includin me- in General Maths forum) will give u same solution unless a Genius finds other way to do

https://www.physicsforums.com/showthread.php?s=&threadid=12588

krab
Science Advisor

Originally posted by himanshu121
In how many forums u have posted this Que it is already in Maths And Homework Section And in fact Krab and everyone(includin me- in General Maths forum) will give u same solution unless a Genius finds other way to do
I agree. I like to help out, but you've posted to 4 separate forums and so my reply was a waste of time on my part. So welcome to my Ignore list.

Hey Guys,

I think I've been wasting my time too.
But, let's not be too harsh on ol' jimmy. He's only posted a couple of times and might not have appreciated why double-posting is such a pain in the XXX.

Hopefully, he does now.
Paul.

Sorry

I really appreciate all the help. I'm new to forum etiquette and I apologize for wasting your time. I will, in the future (hopefully I won't need anymore help, but I doubt that that will happen) not post a message numerous times like I did last time.

Once again, sorry for being a dunce. Thanks.