What is the minimum energy needed to change the speed of a 1600 kg sport utility vehicle from 15.0 m/s to 40.0 m/s?
Well, buckle up because we're going on a wild ride! To calculate the minimum energy needed, we can use the kinetic energy formula. The change in kinetic energy equals the final kinetic energy minus the initial kinetic energy.
So, let's calculate! The initial kinetic energy of the SUV is ½ * mass * (initial velocity)^2, and the final kinetic energy is ½ * mass * (final velocity)^2.
Plugging in the numbers, we get:
Initial kinetic energy = 0.5 * 1600 kg * (15.0 m/s)^2
Final kinetic energy = 0.5 * 1600 kg * (40.0 m/s)^2
Now, let's subtract the initial kinetic energy from the final kinetic energy to find the change in kinetic energy. That will give us the minimum energy needed to change the speed.
Warning: Math ahead!
Change in kinetic energy = Final kinetic energy - Initial kinetic energy
Change in kinetic energy = (0.5 * 1600 kg * (40.0 m/s)^2) - (0.5 * 1600 kg * (15.0 m/s)^2)
Doing the calculations, I'm getting a value of approximately 1,312,000 Joules as the minimum energy needed. Phew! That's some serious energy to go from 15.0 m/s to 40.0 m/s! Mind your speed limits, folks!
To calculate the minimum energy needed to change the speed of a vehicle, we need to use the kinetic energy equation. The kinetic energy (KE) of an object is given by the formula:
KE = 1/2 * mass * velocity^2
Given:
Mass (m) = 1600 kg
Initial velocity (v1) = 15.0 m/s
Final velocity (v2) = 40.0 m/s
Step 1: Calculate the initial kinetic energy (KE1) of the vehicle using the initial velocity:
KE1 = 1/2 * m * v1^2
Step 2: Calculate the final kinetic energy (KE2) of the vehicle using the final velocity:
KE2 = 1/2 * m * v2^2
Step 3: Calculate the change in kinetic energy (ΔKE) by subtracting the initial kinetic energy from the final kinetic energy:
ΔKE = KE2 - KE1
The minimum energy needed to change the speed of the vehicle is equal to the change in kinetic energy (ΔKE). Let's calculate it:
Step 1: Calculate KE1
KE1 = 1/2 * 1600 kg * (15.0 m/s)^2
Step 2: Calculate KE2
KE2 = 1/2 * 1600 kg * (40.0 m/s)^2
Step 3: Calculate ΔKE
ΔKE = KE2 - KE1
Now, let's calculate ΔKE and find the minimum energy needed.
To find the minimum energy needed to change the speed of the sport utility vehicle, we can use the principle of work-energy theorem. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
The kinetic energy of an object is given by the formula: KE = (1/2) * mass * velocity^2.
First, let's calculate the initial kinetic energy of the sport utility vehicle when it is traveling at a speed of 15.0 m/s. We'll use the given mass of the vehicle, which is 1600 kg.
KE_initial = (1/2) * mass * velocity_initial^2
= (1/2) * 1600 kg * (15.0 m/s)^2
Next, let's calculate the final kinetic energy of the sport utility vehicle when it is traveling at a speed of 40.0 m/s.
KE_final = (1/2) * mass * velocity_final^2
= (1/2) * 1600 kg * (40.0 m/s)^2
Now, subtract the initial kinetic energy from the final kinetic energy to find the change in kinetic energy:
ΔKE = KE_final - KE_initial
Finally, substitute the values we calculated into the equation to find the minimum energy needed to change the speed:
Minimum energy = ΔKE
You can now calculate the minimum energy needed to change the speed of the sport utility vehicle from 15.0 m/s to 40.0 m/s by plugging in the values into the equations described above.
Energy = KE2-KE1 = 0.5m*V2^2-0.5m*V1^2 =
800*40^2 - 800*15^2 = 1,100,000 J.