# Solved: Kinematics Problem: Final Velocity

• aaronfue
In summary: No, the change in velocity will be in the same direction as the acceleration vector, but the final velocity will have its own angle (with respect to the x-axis). Work out the angle of the velocity vector from your calculated components of the velocity vector.
aaronfue

## Homework Statement

A hovercraft is traveling 3m/s at 180 deg. The fan of the hovercraft causes a=4m/s2 at 50° for 10 seconds.

## Homework Equations

What is the final velocity?

## The Attempt at a Solution

v = 3cos180 - 4cos50*10?

aaronfue said:

## Homework Statement

A hovercraft is traveling 3m/s at 180 deg. The fan of the hovercraft causes a=4m/s2 at 50° for 10 seconds.

## Homework Equations

What is the final velocity?

## The Attempt at a Solution

v = 3cos180 - 4cos50*10?

The velocity and acceleration should be vectors with both x and y components. Your attempt doesn't appear to deal with the y-component of the acceleration and its contribution to the final velocity (which will be a vector).

gneill said:
The velocity and acceleration should be vectors with both x and y components. Your attempt doesn't appear to deal with the y-component of the acceleration and its contribution to the final velocity (which will be a vector).

So do I have to use the same equation with 4sin50° to get the velocity in the y direction, then I can take the magnitude of both vx & vy to get the final velocity?

Do I have to do the same for the velocity using 3sin180?

aaronfue said:
So do I have to use the same equation with 4sin50° to get the velocity in the y direction, then I can take the magnitude of both vx & vy to get the final velocity?

Do I have to do the same for the velocity using 3sin180?

Sure, sounds good.

A note on terminology: In general, "velocity" is a vector which has both speed and direction. The magnitude of a velocity vector is the speed. Speed is a scalar quantity with no particular associated direction.

gneill said:
Sure, sounds good.

A note on terminology: In general, "velocity" is a vector which has both speed and direction. The magnitude of a velocity vector is the speed. Speed is a scalar quantity with no particular associated direction.

Ok. I calculated the velocity like so:

vx = 3cos180 + 4cos50*10 = 22.71 m/s
vy = 3sin180 + 4sin50*10 = 30.64 m/s

v = √22.712 + 30.642 = 38.14 m/s --> speed

I was thinking...should I use 130° instead of 50°, since the acceleration will be in the same direction as the velocity?

aaronfue said:
Ok. I calculated the velocity like so:

vx = 3cos180 + 4cos50*10 = 22.71 m/s
vy = 3sin180 + 4sin50*10 = 30.64 m/s

v = √22.712 + 30.642 = 38.14 m/s --> speed
That looks fine.
I was thinking...should I use 130° instead of 50°, since the acceleration will be in the same direction as the velocity?
No, the change in velocity will be in the same direction as the acceleration vector, but the final velocity will have its own angle (with respect to the x-axis). Work out the angle of the velocity vector from your calculated components of the velocity vector.

## 1. How do I calculate final velocity in a kinematics problem?

To calculate final velocity in a kinematics problem, you will need to use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Simply plug in the known values and solve for v.

## 2. What units should I use for final velocity in a kinematics problem?

The units for final velocity in a kinematics problem will depend on the units used for the other variables in the problem. Generally, velocity is measured in meters per second (m/s) or kilometers per hour (km/h).

## 3. Can I use the final velocity calculated in a kinematics problem for a different problem?

Yes, the final velocity calculated in a kinematics problem can be used for other problems as long as the variables and units are consistent. However, keep in mind that the final velocity may change if the initial conditions or other factors in the problem change.

## 4. How do I know if my final velocity is accurate in a kinematics problem?

In a kinematics problem, the final velocity is considered accurate if it follows the laws of physics and is supported by the given variables and equations. It is important to double check your calculations and make sure they are consistent and reasonable.

## 5. Can I use the final velocity to determine the distance traveled in a kinematics problem?

Yes, you can use the final velocity to determine the distance traveled in a kinematics problem by using the formula s = ut + 1/2at^2, where s is the distance traveled, u is the initial velocity, a is the acceleration, and t is the time. Again, make sure to use consistent units when plugging in the values.

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