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## 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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