# Kinetic Energy and Power Estimates for
Linear Motion

Problem Overview

The objective of this analysis is to approximate the amount
of energy and power needed for linear motion of a cart.

The cart will need to travel a distance L in specified amount of
time.

This analysis only
determines the amount of energy and power needed to accelerate and move the cart in the specified time. This is a rough analysis since it neglects friction, but it is useful for selecting a viable energy source.

** **

Variables:

mass of car: m
= 10kg (kilograms)

distance
car needs to move: L = 2m (meters)

desired time of travel: t = 5s

Assumptions:

- Energy
loss due to friction is negligible
- The
cart will accelerate at a constant acceleration, which requires the least amount of power to reach a designated speed.

### Energy and Power Analysis

In order to determine the required energy we need to calculate the kinetic energy that will be transferred to the car, but to do this we need to find the maximum velocity of the car.

The average velocity, V_{ave}, is given by distance traveled over time which is:

Typically the cart will use a motor to generate an acceleration force between the wheel and the ground. The required torque of the motor will depend on the drive train mechanism and may include factors such as wheel size and gear ratios.The specific torque can be analyzed with a Free Body Diagram. In the case of a direct attachment between a motor and a wheel the necessary torque is equal to Fr_{wheel}, where rwheel is the radius of the wheel. More complex drivetrains and consideration of traction between the wheel and ground will be shown in future examples.