Kinematics question - which equation to use?

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In summary, the equations x = x0 + v0t + 1/2at^2 and Δx = v0Δt + 1/2a(Δt)^2 are equivalent and can be used to solve for the time an object takes to reach the ground when thrown upward with a given initial velocity and acceleration. It is important to pay attention to units, as using the incorrect unit for acceleration can lead to incorrect solutions.
  • #1
chjoe0
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A ball is thrown upward with velocity 30 ft/s on the roof of a 50 ft building - find the total time until the object meets the ground.

Heres my problem - I used the equation
x = (xsub0) + (vsub0)t + 1/2(a)t^2
I set xsub0 = 50, vsub0 = 30, and a = -9.8
I solved for t when x = 0, but the book gave a totally different answer.

Then I went back and used the equation given in the book:
[tex]\Delta[/tex]x = (vsubnot)[tex]\Delta[/tex]t + 1/2(a)([tex]\Delta[/tex]t)^2

I solved for [tex]\Delta[/tex]t when [tex]\Delta[/tex]x = 50, and my answer agreed
with the textbook solution...

My question is, why does the 2nd equation work in this situation, and how do I know when it is appropriate to use which?
 
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  • #2
Those equations are equivalent. Used properly, you get the same answer for each. (If you got different answers, show exactly what you did.) Note that with the usual sign convention (up is +), [itex]\Delta x[/itex] should be -50.

Also: what are your units? If distance is in feet, then acceleration should be 32 ft/s^2, not 9.8 m/s^2.
 
  • #3
Also: what are your units? If distance is in feet, then acceleration should be 32 ft/s^2, not 9.8 m/s^2.

i think that was my error :blushing:
thank you very much - it works out now
 

1. What is kinematics and why is it important?

Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion. It is important because it helps us understand and predict the movement of objects, which is essential in many fields such as engineering, biomechanics, and robotics.

2. What are the three equations of kinematics?

The three equations of kinematics are:

  • Position equation: x = x0 + v0t + 1/2at2
  • Velocity equation: v = v0 + at
  • Acceleration equation: v2 = v02 + 2a(x-x0)

These equations are used to describe the relationship between an object's position, velocity, acceleration, and time.

3. How do I know which equation to use for a kinematics problem?

To determine which equation to use, you need to identify what information is given in the problem and what you are trying to find. If you have the initial and final position, use the position equation. If you have the initial and final velocity, use the velocity equation. If you have the initial velocity, final velocity, and acceleration, use the acceleration equation.

4. Can I use more than one equation for a kinematics problem?

Yes, you can use more than one equation for a kinematics problem. In fact, it is often necessary to use multiple equations to solve a problem, especially if you are trying to find multiple unknowns.

5. Are there any common mistakes to avoid when using kinematics equations?

One common mistake is using the wrong equation for the given problem. Make sure to carefully read and interpret the problem to determine which equation to use. Another mistake is not paying attention to the units of the variables in the equations. Make sure to use consistent units throughout your calculations.

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