Impulse-Momentum Theorem and acceleration

[92_stealth]

Impulse-Momentum Theorem...

Homework Statement

So here's the problem:
a 3.00 kg object has velocity 7.00 j m/s. Then, a total force of 12.0i N acts on the object for 5 seconds.
A.Calculate the object's final velocity using the impulse momentum theorem.
b. calc its acceleration from a = (vf - vi) / delta t.
c. calculate its acceleration from a = F/m

Homework Equations

<given in question>

I really don't know what to use for impulse-momentum theorem in a? Any and all help is appreciated...

 

[LowlyPion]

Welcome to PF.

F = m*a = m*Δv/Δt

F*Δt = m*Δv = Δp

So in a, you have F and Δt. That gives you Δp

 

[nlightner]

The Impulse-Momentum Theorem states that the impulse applied to an object is equal to the change in momentum of the object. In this case, the impulse applied is equal to the force multiplied by the time it acts for. Therefore, we can use the equation P = FΔt to calculate the change in momentum.

a. To calculate the object's final velocity, we can use the equation P = mv, where m is the mass of the object and v is its velocity. We can rearrange this equation to solve for v, giving us v = P/m. From part a, we know that P = FΔt, so we can substitute that into the equation to get v = (FΔt)/m. Plugging in the given values, we get v = (12.0i N * 5 s)/3.00 kg = 20.0i m/s. This is the object's final velocity.

b. To calculate the acceleration, we can use the equation a = (vf - vi)/Δt, where vf is the final velocity, vi is the initial velocity, and Δt is the change in time. From part a, we know that vf = 20.0i m/s. The initial velocity, vi, is given as 7.00 j m/s, so we can write that as vi = 7.00j m/s. Plugging these values into the equation, we get a = (20.0i m/s - 7.00j m/s)/5 s = (20.0i m/s)/5 s = 4.00i m/s^2. This is the object's acceleration.

c. We can also calculate the acceleration using the equation a = F/m, where F is the force and m is the mass of the object. From the given values, we know that F = 12.0i N and m = 3.00 kg. Plugging these values into the equation, we get a = (12.0i N)/(3.00 kg) = 4.00i m/s^2. This is the same result as part b, which confirms our calculation.