Question: User: is this correct On a number line, you move from a position mark of $87.0$ m [E] to another position mark of $65.0$ m [W], then to another position mark of $26.0$ m [E].
What is your overall displacement vector (in m)?
Show your work and steps. There is no need at all to show a diagram (for the 1-D line) with your solution. Just make sure that your solution steps reflect how they would look like if a diagram was shown.
You can copy/paste "$\Delta$" wherever you need in your solution. Also, do not worry about putting an arrow "$\to$" on top of the displacement symbol (it can't be shown on a Google form).
2 points
Let [E] (east) = positive direction
Let [W] (west) = negative direction
first displacement ($\Delta d_1$): from $87.0$ m [E] (so its positive) to $65.0$ m [W] (so its negative)
-----> $\Delta d_1=df-di$ ------> $\Delta d_1= 65.0$ [W] $- 87.0$[E]$= -152$ -------> $\Delta d_1= -65.0$[E] $- 87.0$[E]$= -152$[E] -------> $152$ m [W]
second displacement ($\Delta d_2$): from $65.0$ m [W] (so its negative) to $26.0$ m [E] (so positive)
-----$\Delta d_2=df-di$ ------> $\Delta d_2= 26.0$ [E] $- 65.0$[W]$= 91.0$----->$\Delta d_2= 26.0$ [E] $+ 65.0$ [E] $= 91.0$ m [E]
total displacement ($\Delta d$): $\Delta d=\Delta d_1+\Delta d_2$ ------> $\Delta d= 91.0$ [E] $+152$ [W] ----> $\Delta d= 91.0$ [E] $-152$ [E] $= -61.0$ m [E]----> so final answer is $\Delta d=61.0$ m [W] or $-61.0$ m [E]
1. **State the problem:**
Calculate the overall displacement vector when moving from $87.0$ m [E] to $65.0$ m [W], then to $26.0$ m [E] on a number line.
2. **Define directions:**
Let [E] (east) be positive and [W] (west) be negative.
3. **Calculate first displacement $\Delta d_1$:**
$$\Delta d_1 = d_f - d_i = (-65.0) - 87.0 = -152.0 \text{ m}$$
Here, $65.0$ m [W] is $-65.0$ m.
4. **Calculate second displacement $\Delta d_2$:**
$$\Delta d_2 = d_f - d_i = 26.0 - (-65.0) = 26.0 + 65.0 = 91.0 \text{ m}$$
5. **Calculate total displacement $\Delta d$:**
$$\Delta d = \Delta d_1 + \Delta d_2 = -152.0 + 91.0 = -61.0 \text{ m}$$
6. **Interpret the result:**
Since $\Delta d$ is negative, the displacement is $61.0$ m [W].
**Final answer:**
$$\boxed{\Delta d = -61.0 \text{ m [E]} = 61.0 \text{ m [W]}}$$