I won't do that again.Problem: Integrating Kinematic Equations to Find Position

In summary, the conversation is about solving a problem involving a car's acceleration and position at a given time using integrals and equations for acceleration, velocity, and position. There is confusion about the initial position and whether or not integration is necessary. Ultimately, it is determined that the equations given are only valid when acceleration is constant and the conversation ends with a clarification on the problem.
  • #1
jjiimmyy101
74
0
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). But how do you do this.
 
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  • #2
Forget numbers for a minute.

If ao is acceleration, vo is initial velocity, xo is initial position, then,

Acceleration at time t is: a(t) = ao
Velocity at time t is: v(t) = vo + ao * t
Position at time t is: x(t) = xo + vo * t + (ao * t^2)/2


They haven't taught you integration yet. Maybe you've been given these formulae, though, or something similar.
 
  • #3
what's the initial position (xo)?
 
  • #4
You don't need to know to answer the question. It's the distance, d, that's needed ...
d = x(4) - xo
= ...
 
  • #5
d = 24s^-1/3

Sorry, I'm still not understanding.
I really appreciate your help, though.
 
  • #6
How far you go doesn't depend on where you start from, so take xo to be as simple as possible ... xo = 0.
 
  • #7
Originally posted by pnaj
Forget numbers for a minute.

If ao is acceleration, vo is initial velocity, xo is initial position, then,

Acceleration at time t is: a(t) = ao
Velocity at time t is: v(t) = vo + ao * t
Position at time t is: x(t) = xo + vo * t + (ao * t^2)/2


They haven't taught you integration yet. Maybe you've been given these formulae, though, or something similar.

The equations are valid only when a is constant
 
  • #8
Thanks for that, himanshu121, I didn't notice the 's' sitting in the expression for a.

I just assumed that it was just a simple problem that didn't need integration and got side-tracked into seeing if jimmy had seen these equations before.
 

1. What is kinematics of a particle?

Kinematics of a particle is the study of the motion of a single object without considering the forces that cause the motion. It involves analyzing the position, velocity, and acceleration of the particle over time.

2. What are the three main quantities used in kinematics?

The three main quantities used in kinematics are position, velocity, and acceleration. Position refers to the location of the particle in space, velocity refers to the rate of change of position, and acceleration refers to the rate of change of velocity.

3. What is the difference between average and instantaneous velocity?

Average velocity is the total displacement of a particle divided by the total time taken, while instantaneous velocity is the velocity of the particle at a specific moment in time. Average velocity gives an overall picture of the motion, while instantaneous velocity gives a more precise measure at a particular point.

4. How is acceleration related to velocity?

Acceleration is the rate of change of velocity. This means that the acceleration of a particle is directly proportional to the change in its velocity over time. If the velocity is changing at a constant rate, the acceleration will also be constant. If the velocity is changing at a changing rate, the acceleration will also be changing.

5. What is the difference between linear and angular kinematics?

Linear kinematics deals with the motion of an object in a straight line, while angular kinematics deals with the motion of an object in a circular path. Linear kinematics involves the study of position, velocity, and acceleration along a straight line, while angular kinematics involves the study of position, velocity, and acceleration along a circular path.

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