a 1200kg car is moving on the freeway at 30 m/s. (a) Find the magnitude of its momentum and its kinetic energy in SI units. (b) At what speed, in m/s, will the car's momentum be half of what it is in part (a). (c) At what speed, in m/s, will the cars kinetic energy be half of what it is in part (a)

(a) Well, well! Let's calculate the magnitude of the car's momentum first. Remember, momentum equals mass times velocity. So, the momentum would be 1200 kg times 30 m/s, giving us a grand total of 36,000 kg m/s. As for the kinetic energy, that's given by the formula 1/2 times mass times velocity squared. Plug in the numbers, and we get 1/2 times 1200 kg times (30 m/s)^2, which equals 540,000 Joules of energy.

(b) Ah, you want the car's momentum to be half of what it is in part (a)? Well, remember that momentum is directly proportional to velocity. So, if you halve the momentum, you'll also halve the velocity. Therefore, the car's speed would be 15 m/s.

(c) Now, if you want the car's kinetic energy to be half of what it is in part (a), you need to consider the relationship between kinetic energy and velocity squared. Since kinetic energy is proportional to velocity squared, you'll need to find a velocity that results in half the kinetic energy. Square root that, and you'll have your answer! Let's do the math: the square root of (540,000 J divided by 2) divided by 1200 kg is approximately 22.36 m/s.

There you have it! I hope you enjoyed the ride with these calculations. Just remember, if life gets too fast, take a moment-um to laugh!

(a) To find the magnitude of the car's momentum, we use the equation: momentum (p) = mass (m) × velocity (v).

Given:
Mass (m) = 1200 kg
Velocity (v) = 30 m/s

Using the formulas, we can calculate:

Momentum (p) = mass × velocity
= 1200 kg × 30 m/s
= 36,000 kg·m/s

Therefore, the magnitude of the car's momentum is 36,000 kg·m/s.

To calculate the car's kinetic energy, we use the equation: kinetic energy (KE) = 0.5 × mass × velocity^2.

Given:
Mass (m) = 1200 kg
Velocity (v) = 30 m/s

Using the formula, we can calculate:

Kinetic Energy (KE) = 0.5 × mass × velocity²
= 0.5 × 1200 kg × (30 m/s)^2
= 540,000 J

Therefore, the car's kinetic energy is 540,000 Joules (J) in SI units.

(b) To find the speed at which the car's momentum is half of what it is in part (a), we set up the equation:

Momentum (p2) = 0.5 × Momentum (p1)

Let the speed be represented by v2.

Given:
Momentum (p2) = 0.5 × 36,000 kg·m/s
Mass (m) = 1200 kg
Velocity (v2) = ?

Using the formula for momentum, we can substitute and solve for v2:

p2 = mv2
0.5 × 36,000 kg·m/s = 1200 kg × v2

Simplifying the equation:

18,000 kg·m/s = 1200 kg × v2

Divide both sides by 1200 kg:

v2 = 18,000 kg·m/s ÷ 1200 kg
v2 = 15 m/s

Therefore, the speed at which the car's momentum is half of what it is in part (a) is 15 m/s.

(c) To find the speed at which the car's kinetic energy is half of what it is in part (a), we set up the equation:

Kinetic Energy (KE2) = 0.5 × Kinetic Energy (KE1)

Let the speed be represented by v3.

Given:
Mass (m) = 1200 kg
Velocity (v3) = ?

Using the formula for kinetic energy, we can substitute and solve for v3:

0.5 × mass × v3^2 = 0.5 × 540,000 J

Simplifying the equation:

v3^2 = 540,000 J ÷ (0.5 × 1200 kg)
v3^2 = 900 m²/s²

Taking the square root of both sides:

v3 = √(900 m²/s²)
v3 = 30 m/s

Therefore, the speed at which the car's kinetic energy is half of what it is in part (a) is 30 m/s.

To solve these problems, we will use the formulas for momentum and kinetic energy.

(a) The formula for momentum is given by:

Momentum (p) = mass (m) x velocity (v)

Given:
Mass (m) = 1200 kg
Velocity (v) = 30 m/s

Substituting the values into the formula:

Momentum (p) = 1200 kg × 30 m/s
= 36,000 kg·m/s

Therefore, the magnitude of the car's momentum is 36,000 kg·m/s.

To calculate the kinetic energy, we will use the formula:

Kinetic energy (KE) = (1/2) × mass (m) × velocity² (v²)

Given:
Mass (m) = 1200 kg
Velocity (v) = 30 m/s

Substituting the values into the formula:

Kinetic energy (KE) = (1/2) × 1200 kg × (30 m/s)²
= (1/2) × 1200 kg × 900 m²/s²
= 540,000 J

Therefore, the car's kinetic energy in SI units is 540,000 J.

(b) Now, we need to find the speed at which the car's momentum is half of what it is in part (a).

Let's assume the new speed as v'.

Using the formula for momentum, we can write:

Momentum (p') = 1200 kg × v'

We need to find v' when p' is half of the initial momentum (p).

So, p' = (1/2) × p

Substituting the values into the equation:

(1/2) × p = 1200 kg × v'

Simplifying the equation:

v' = [(1/2) × p] / 1200 kg

Substituting the value of p from part (a):

v' = [(1/2) × 36,000 kg·m/s] / 1200 kg

v' = 30 m/s

Therefore, the speed at which the car's momentum will be half of what it is in part (a) is 30 m/s.

(c) Next, we need to find the speed at which the car's kinetic energy is half of what it is in part (a).

Using the formula for kinetic energy, we can write:

Kinetic energy (KE') = (1/2) × 1200 kg × (v')²

We need to find v' when KE' is half of the initial kinetic energy (KE).

So, KE' = (1/2) × KE

Substituting the values into the equation:

(1/2) × KE = (1/2) × 540,000 J

Simplifying the equation:

v'² = [(1/2) × KE] / (1200 kg)

Substituting the value of KE from part (a):

v'² = [(1/2) × 540,000 J] / (1200 kg)

v'² = 225 m²/s²

Taking the square root of both sides:

v' = √225 m/s
= 15 m/s

Therefore, the speed at which the car's kinetic energy will be half of what it is in part (a) is 15 m/s.

momentum = m v = 1200 * 30 kg m/s

Ke = (1/2) m v^2 = 600 * 900 Joules

30/2 = 15

v^2 = (1/2)30^2 = 900/2 = 450
so
v = sqrt (450) = sqrt (9*50) = sqrt(3*3*5*5*2) = 15 sqrt 2
v = 21.2 m/s