**Problem**

**Part 1:** The average acceleration is defined as

- .

Rearrange this equation (with defined quantities) to show that .

**Part 2:** The average velocity is define as

- .

When the average acceleration is constant, the average velocity is

- .

Use the result in part 1 and the above formulas for average velocity to show that

- .

**Part 3:** Use the results in part 1 and part 2 to show that

- .

**Solution**

**Part 1**

Let be a time interval and .

Isolating for yields

- .

**Part 2**

Let be a time interval and .

When the average acceleration is constant

Since for constant average acceleration

**Part 3**

Isolate for time from the result of part 1

From part 2

Thus

- .

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