Examples

Example: Predicting the location of a object undergoing constant velocity motion

A cart is given a slight push along a near frictionless track (as shown in the video below).

After the push, the cart is observed to move with a near constant velocity ${\overrightarrow{v}}_{cart} = \langle 1.2,0,0\rangle\frac{m}{s}$. Determine its location after 3 seconds.

Setup

You need to predict the location of the cart using the information provided and any information that you can collect or assume.

Facts

• The cart moves to the right.
• The cart’s velocity is given by ${\overrightarrow{v}}_{cart} = \langle 1.2,0,0\rangle\frac{m}{s}$.

Lacking

• The initial location of the cart is not known.

Approximations & Assumptions

• The interactions of the cart with its surroundings, over the interval that you care about, are negligible. That is, the cart moves with a constant velocity.
• As a result, the average and instantaneous velocity are equivalent.
• We will assume the initial location of the cart is ${\overrightarrow{r}}_{i}$.

Representations

• The location of the cart can be predicted using the position update formula, ${\overrightarrow{r}}_{f} = {\overrightarrow{r}}_{i} + {\overrightarrow{v}}_{avg}\Delta t$
• The motion of the cart is represented using the following motion diagram.

Solution

We can compute the final location,

You might use the video to define an origin such that the initial position of the cart is ${\overrightarrow{r}}_{i} = \langle 0.4,1.1,0\rangle m$. With that new information, the final location of the cart can be computed exactly,

.

Notice that $y$-position of the cart remained unchanged because all the motion of the cart was in the $x$-direction.