Word Problem with Kinematics Equation

The exact time is 1.0204081633... seconds, which you should use to get delta x = -15 meters.In summary, the object thrown from a cliff with an initial velocity of 10 m/s reaches a final velocity of 20 m/s downward as it lands. With an acceleration due to gravity of 9.8 m/s^2, the object's displacement is -15 meters and it takes 1.0204081633... seconds to land.
  • #1
Natko
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Homework Statement


An object thrown up from a cliff 10 m/s reaches a velocity of 20 m/s [down] as it lands. If acceleration due to gravity is 9.8 m/s2, what is the object's displacement? How long did it take for the object to land from the time it was thrown?


Homework Equations


I'm not sure if all of the below are relevant, or perhaps some equations are missing.

Δx = v0t + 1/2at2
(displacement = initial velocity x time + 1/2 acceleration x time squared)

vf2 = v02 + 2aΔx
(final velocity squared = initial velocity squared + 2 acceleration x displacement


The Attempt at a Solution


t1 = v/a = 1.02 s
t2 = v/a = 2.04 s
t1 + t2 = 3.1 s

Not sure how to find the displacement, but the answer key says it's -15m. How do I find it?
 
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  • #2
Natko said:
Not sure how to find the displacement, but the answer key says it's -15m. How do I find it?
You can use either of your two equations to solve for the displacement. If you use the first, do not round off the time to 3.1 seconds.
 
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1. What is a kinematics equation?

A kinematics equation is a mathematical formula that describes the motion of an object in terms of its position, velocity, and acceleration. It is commonly used in physics to solve word problems related to motion.

2. What are the three basic kinematics equations?

The three basic kinematics equations are the equations of motion for constant acceleration, also known as the SUVAT equations. They are:

  • s = ut + 0.5at2 (equation for displacement)
  • v = u + at (equation for final velocity)
  • v2 = u2 + 2as (equation for average velocity)

3. How do I use kinematics equations to solve a word problem?

To solve a word problem using kinematics equations, first identify the given information (initial velocity, final velocity, acceleration, etc.) and the unknown variable. Then, choose the appropriate kinematics equation and plug in the known values. Solve for the unknown variable using algebraic manipulation.

4. What are some common units used in kinematics equations?

The common units used in kinematics equations are:

  • Displacement: meters (m)
  • Velocity: meters per second (m/s)
  • Acceleration: meters per second squared (m/s2)
  • Time: seconds (s)
It is important to make sure all units are consistent when using kinematics equations.

5. Can kinematics equations be used for non-constant acceleration?

Yes, kinematics equations can be used for non-constant acceleration, but they will only give an average value for the acceleration. In these cases, calculus may be needed to find the exact values of velocity and displacement at a specific time.

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