HELP PLEASE PLEASE A 1.50 × 103 kilogram car is traveling east at 20 meters per second. The brakes are applied and the car is brought to rest in 5.00 seconds.
Calculate the magnitude of the impulse applied to the car to bring it to rest.

Calculate the force on the car.

Magnitude of Impulse: 30000 kg · m/s or 30000 N · s

Force on the Car: -6000 N

General Formulas and Concepts:

Math

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of Equality

Physics

Momentum

Momentum Equation: P = mvImpulse Equation: J = FΔtLaw of Conservation of MomentumExplanation:

Step 1: Define

Mass m = 1.50 × 10³ kg

Velocity v = 20 m/s east

Change in time Δt = 5.00 s

Step 2: Find Magnitude

Substitute [Momentum]:                    P = (1.50 × 10³ kg)(20 m/s)Multiply:                                              P = 30000 kg · m/s

Step 3: Find Force

We use the Law of Conservation of Momentum to find our break force acting upon the car.

Substitute [Impulse]:                    30000 kg · m/s = F(5.00 s)Rewrite:                                        30000 N · s = F(5.00 s)Divide 5 on both sides:               6000 N = FRewrite:                                        F = 6000 N

Since the car is deaccelerating, the break force would be towards the west direction (negative as east is our positive direction).

∴ F = -6000 N

| impulse | = 30000 N * s

force = -6000 N

Explanation:

The Impulse-Momentum Theorem states that the impulse applied to an object is equal to the change in momentum of the object. Therefore,

FΔt = mΔv where FΔt = impulse & mΔv = change in momentum

We can use either side of the equation to find the impulse of the object. Since we don't have the force applied to the object, we can use the right side:

Δp = mΔv where Δp = change in momentum, m = mass (kg), and Δv = change in velocity

We are given the mass of the car and the initial and final velocity. Let's set the right direction to be positive and the left direction to be negative.

m = 1.50 * 10³ = 1500 kg Δv = 0 m/s - 20 m/s = -20 m/s

Substitute the known values into the equation.

Δp = (1500)(-20) Δp = -30000  

The magnitude of the impulse applied to the car to bring it to rest is |-30000| = 30000 N * s.

We can derive the force from the Impulse-Momentum Theorem by dividing both sides by Δt.

F =  (mΔv)/Δt

We know the mass of the car, the change in velocity, and the time elapsed.

Substitute the known values into the equation:

F = [(1500)(-20)]/5.00  F = [-30000]/5.00 F = -6000

The force on the car is -6000 N.

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