Final answer:
To calculate the speed at which an object must travel for its total energy to be 1% more than its rest energy, we use the equation E = mc² and set up an equation where the total energy is 1.01 times the rest energy. Solving for the speed, we find that the object must travel at approximately 0.1 times the speed of light.
Step-by-step explanation:
To calculate the speed at which an object must travel for its total energy to be 1% more than its rest energy, we need to consider the equation for the total energy of an object:
E = mc²
Where E is the total energy, m is the mass of the object, and c is the speed of light. Since we want the total energy to be 1% more than the rest energy, we can set up the following equation:
E = 1.01(mc²)
Now, we can plug in the rest energy of the object and solve for the speed:
Rest energy = mc²
0.01mc² = mc²
0.01c² = c²
0.01 = 1
c = √(0.01)
c = 0.1
Therefore, the object must travel at approximately 0.1 times the speed of light for its total energy to be 1% more than its rest energy.