A car has a kinetic energy of 1.9 × 103 joules. If the velocity of the car is decreased by half, what is its kinetic energy?
1/2 m(v/2)^2 = 1/2 m*v^2/4 = 1/4 (1/2 mv^2)
so, halving the velocity reduces the KE by a factor of 4.
To find the new kinetic energy of the car when its velocity is decreased by half, we need to use the formula for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Since the mass of the car is not given, we can assume it is constant. Therefore, the mass does not affect the change in kinetic energy.
Let's denote the initial velocity of the car as v and the final velocity as (1/2) v.
The initial kinetic energy (KE_i) is given as 1.9 × 10^3 joules.
Using the formula for kinetic energy, we have:
KE_i = (1/2) * mass * v^2
To find KE_f, the final kinetic energy, we substitute v/2 for v:
KE_f = (1/2) * mass * (v/2)^2
Simplifying the equation further, we get:
KE_f = (1/2) * mass * (1/4) * v^2
We can combine the constants:
KE_f = (1/8) * mass * v^2
Therefore, the new kinetic energy of the car when its velocity is decreased by half is one-eighth of the initial kinetic energy.
KE_f = (1/8) * KE_i
Plugging in the value of KE_i = 1.9 × 10^3 joules, we get:
KE_f = (1/8) * 1.9 × 10^3 joules
Calculating the value, we find:
KE_f ≈ 2.375 × 10^2 joules
Therefore, the new kinetic energy of the car is approximately 2.375 × 10^2 joules.
To find the kinetic energy of the car after its velocity is decreased by half, we need to use the equation for kinetic energy:
Kinetic Energy = 1/2 * mass * velocity^2
First, let's assume that the mass of the car remains the same. This means that the only variable that changes is the velocity.
Given that the car initially has a kinetic energy of 1.9 × 10^3 joules, we can substitute this value into the equation and solve for the initial velocity.
1.9 × 10^3 = 1/2 * mass * (initial velocity)^2
Since we don't have the exact values for the mass and initial velocity, we won't be able to calculate them directly. However, we can make use of the fact that the final velocity will be half the initial velocity to find the final kinetic energy.
Let's assume the initial velocity is v and the final velocity is v/2. We can rewrite the equation as:
1.9 × 10^3 = 1/2 * mass * (v)^2
Now, let's find out the kinetic energy when the velocity is decreased by half:
Final Kinetic Energy = 1/2 * mass * (v/2)^2
Simplifying this equation further, we have:
Final Kinetic Energy = 1/2 * mass * (1/4 * v^2)
Final Kinetic Energy = 1/8 * mass * v^2
So, if the velocity of the car is decreased by half, the kinetic energy will be 1/8 of the original kinetic energy.