How to find final velocity?

In summary, a body with a mass of 9.30 kg and an initial velocity of 9.30 m/s decelerates uniformly for 9.30 seconds, ending up 9.30 m from its starting point. The final speed of the body can be found using the kinematic equation d=1/2(vf+vi)t, which can be solved for V_f to find the instantaneous speed. This is different from average speed, which is found by dividing distance by time.
  • #1
ScienceGirl90
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0

Homework Statement


An 9.30 kg body moving at 9.30 m/s begins to decelerates uniformly. After 9.30 s the body is 9.30 m from the location were it started to decelerate.
What is the final speed of the body 9.30 s after it started to decelerate?


Homework Equations


I'm not sure what equation to use.


The Attempt at a Solution


I'm not sure how to tackle this problem to find final velocity when I only have initial velocity, time, and distance. Help please!
 
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  • #2
You can use a couple of the kinematic equations, but there is a single simple kinematic equation for constant acceleration that relates initial velocity, final velocity, displacement, and time. Which one is that?
 
  • #3
Would that be the d=1/2(vf+vi)t ?
I wasn't given that equation on my handout but I looked it up.
 
  • #4
Speed is the magnitude of the velocity. Yes, that is the right equation; solve it for V_f; the magnitude of V_f is its speed. Speed is not distance divided by time. Distance divided by time is average speed. You are looking for the instantaneous speed.
 
  • #5


As a scientist, the first step in finding the final velocity is to identify the relevant equations that relate to the given information. In this case, the body is undergoing uniform deceleration, so the equation that relates initial velocity, final velocity, acceleration, and time is: vf = vi + at. We can rearrange this equation to solve for final velocity: vf = vi + at.

To solve for the final velocity, we need to plug in the known values from the problem. The initial velocity (vi) is given as 9.30 m/s. The time (t) is also given as 9.30 s. However, we do not have the value for acceleration (a) yet.

To find the acceleration, we can use the equation that relates acceleration, initial velocity, final velocity, and displacement: vf^2 = vi^2 + 2ad. We can rearrange this equation to solve for acceleration: a = (vf^2 - vi^2)/2d.

Plugging in the known values for displacement (d = 9.30 m), initial velocity (vi = 9.30 m/s), and final velocity (vf = 0 m/s), we can solve for acceleration: a = (0^2 - 9.30^2)/2(9.30) = -4.5 m/s^2.

Now that we have the value for acceleration, we can plug it back into the first equation (vf = vi + at) to solve for the final velocity: vf = 9.30 m/s + (-4.5 m/s^2)(9.30 s) = 9.30 m/s - 41.85 m/s = -32.55 m/s.

Therefore, the final velocity of the body after 9.30 s is -32.55 m/s. It is important to note that the negative sign indicates that the body is moving in the opposite direction of its initial velocity, which makes sense since it is decelerating.

In conclusion, by using the appropriate equations and plugging in the given values, we were able to find the final velocity of the body after 9.30 s. This process is a fundamental aspect of the scientific method - identifying and using equations to solve problems and gain a better understanding of the physical world.
 

1. What is the formula for finding final velocity?

The formula for finding final velocity is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time interval.

2. How do I find the initial velocity?

To find the initial velocity, you will need to know the final velocity, acceleration, and time interval. Rearrange the formula for final velocity to solve for u: u = v - at.

3. Can I calculate final velocity without knowing the acceleration?

No, you cannot calculate final velocity without knowing the acceleration. The formula for final velocity requires the acceleration as a variable.

4. What units should I use for velocity and time?

Velocity is typically measured in meters per second (m/s) and time is measured in seconds (s). Make sure to use the same units consistently in your calculations to ensure accurate results.

5. How can I use final velocity to determine an object's displacement?

To determine an object's displacement, you will need to know the initial velocity, final velocity, and time interval. Use the formula s = ut + 1/2at^2, where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time interval.

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