Did I do this right an F=ma need to find Initial Speed?

In summary, the conversation discusses finding the initial speed of a car with a mass of 2600 kg and a braking force of 2765N in order to stop at a distance of 3036.3m. The correct calculation is found by using the formula Vi=Vf-at, where Vi is the initial velocity, Vf is the final velocity (which is 0 in this case), a is the acceleration, and t is the time. The initial speed is determined to be -80.3614 m/s, which can be negative depending on how positive is defined.
  • #1
bradycat
13
0
Did I do this right an F=ma need to find Initial Speed?

Need help on this.
A car whose mass is 2600 kg can produce an unbalanced braking force of 2765N.
Calculate the car's initial speed in order to have a stopping distance of 3036.3m.
Vi=?
So...
m=2600kg
F=2765N
s=3036.3m
Vf=0

So I found acceleration of a=F/m = 2765/2600 = 1.06346m/s^2
So I have to find time=Square root of 2(3036.33)/1.06346 = 75.56605s
So I would use this formula to solve for Vi? right
Vi=Vf -at
Vi = 0 - (1.06346)(75.56605) = -80.3614 m/s
Is the negative right?
IS THIS CORRECT if not please show me where I went wrong
Thanks
Jo
 
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  • #2


Where you have found the time you have made a mistake since that formula requires the initial velocity too.
 
  • #3


Kurdt said:
Where you have found the time you have made a mistake since that formula requires the initial velocity too.

Hi Kurdt,
I used the time formula where you use distancex2 over acceleration. THAT is wrong your saying?
What formula should I use?
 
  • #4


Yes, that's wrong. It came from d=v0t + (1/2)at^2; you only get t=sqrt(2d/a) if v0=0, which, in this case, it's not. However, you got the right answer at the end because acceleration is symmetrical with respect to time. That is, if you record a car decelerating to 0 at -1.06 m/s^2 and play the video backwards at 1 second per second, the car would seem to be accelerating at 1.06 m/s^2 to its initial speed. That's why using t=sqrt(2d/a) worked.
 
  • #5


Hi Ideasule.
So the -80.3614 m/s is correct?
So the Vi can have a negative number then?
I thought it could not have a negative on a Vi?
 
  • #6


Velocities and accelerations are vector quantities, so they can certainly be negative. For Vi, yes, -80.36 m/s. If you don't explain the fact about time symmetry, however, you wouldn't get full credit on a test.

Whether Vi is positive or negative depends on which way you define as positive. Here, you used a=1.06 m/s^2, which means you've defined "backwards" as positive. It's not surprising, then, that initial velocity would be negative. (Initial SPEED, however, is not; speed is a scalar.)
 

FAQ: Did I do this right an F=ma need to find Initial Speed?

1. What exactly does F=ma mean?

F=ma is a formula that represents Newton's Second Law of Motion. It states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.

2. Why is it important to use F=ma when finding initial speed?

F=ma is a fundamental equation in physics that helps us understand the relationship between force, mass, and acceleration. By using this formula, we can accurately calculate the initial speed of an object based on its mass and the force acting upon it.

3. Can F=ma be used for any type of motion?

Yes, F=ma can be used for any type of motion, as long as there is a force acting on the object and the mass of the object is known. This equation is not limited to a specific type of motion.

4. Are there any other equations that can be used to find initial speed?

Yes, there are other equations that can be used to find initial speed, such as v=at and v²=u²+2as. However, F=ma is often used in combination with these equations to solve for initial speed in more complex situations.

5. Is it necessary to convert units when using F=ma to find initial speed?

Yes, it is necessary to ensure that all units are consistent when using F=ma to find initial speed. Both the force and mass should be in standard units (such as Newtons for force and kilograms for mass) and the acceleration should be in meters per second squared. This will ensure an accurate calculation of the initial speed.

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