What is the Final Velocity After Deceleration?

[ScienceGirl90]

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!

 

[PhanthomJay]

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?

 

[ScienceGirl90]

Would that be the d=1/2(v_f+v_i)t ?
I wasn't given that equation on my handout but I looked it up.

 

[PhanthomJay]

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.

 

[rwisz]

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.