what is the mass of a vehicle traveling at 25 km/hr with a kinetic energy equal to 1 x 10 to the 4th power J?
V = 25km/h = 25000m/3600s = 6.94 m/s.
KE = 0.5m*V^2 = 10^4 J.
0.5m*6.94^2 = 10000
24.08m = 10000
m = 415.3 kg.
To determine the mass of the vehicle, we can use the equation for kinetic energy:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
In this case, the given kinetic energy is 1 x 10^4 J (joules), and the velocity is 25 km/hr. However, we need to convert the velocity from km/hr to m/s, as the equation requires the value in meters per second.
To convert km/hr to m/s, we can use the conversion factor 1 km = 1000 m and 1 hr = 3600 s.
Step 1: Convert the velocity from km/hr to m/s.
25 km/hr = (25 * 1000 m) / (1 * 3600 s) = 25000 m / 3600 s ≈ 6.94 m/s (rounded to two decimal places)
Now that we have the velocity in m/s, we can rearrange the equation to solve for the mass.
Step 2: Rearrange the equation:
KE = 1/2 * mass * velocity^2
Rearranging, we find:
mass = (2 * KE) / (velocity^2)
Step 3: Substitute the values:
mass = (2 * 1 x 10^4 J) / (6.94 m/s)^2
Step 4: Calculate the mass:
mass = (2 * 10000) / (6.94^2) ≈ 409.20 kg (rounded to two decimal places)
Therefore, the mass of the vehicle traveling at 25 km/hr with a kinetic energy of 1 x 10^4 J is approximately 409.20 kilograms.