Chapter 22, Problem 42A

Decay of radioactive isotopes of thorium and uranium in granite and other rocks in Earth’s interior provides sufficient energy to keep the interior molten, heat lava, and provide warmth to natural hot springs. This is due to the average release of about 0.03 J per kilogram each year. Show that 13.3 million years are required for a chunk of thermally insulated granite to increase $500°C$ in temperature. (Use $800J/kg°C$ for the specific heat capacity of granite.)

To determine

The change in the acceleration of your bicycle while riding from your home to the store

Explanation of Solution

Introduction:

Acceleration means the rate of change of velocity that is how the speed of a body is being changed, but it does not happen always. When an object moves in a circular trajectory at a constant speed, it is still accelerating as the direction of its velocity is changing.

While you are going to the store from home, your acceleration starts changing. Sometimes your acceleration increases and sometimes it decreases, depending on your overall speed

Constant acceleration does not occur because it means that you would constantly accelerate and as a result you eventually go past the store.

Even decrease of speed is a type of acceleration .When you reach it, then only we can calculate how much your velocity was on average and we can also analyze how the changing in acceleration would've affected it.

Conclusion:

Acceleration is the second derivative of distance with respect to time and the first derivative of distance is velocity. Acceleration is zero when the velocity of a body is constant.