Questions: Problem 10: (10% of Assignment Value) A particle's velocity in meters per second along the x-axis is described by v(x)=A x+B x^2, where the position x is in meters. The values of the constants are A= 7.95, and B=-7.4 What are the correct units for constant B?

Problem 10: (10% of Assignment Value) A particle's velocity in meters per second along the x-axis is described by v(x)=A x+B x^2, where the position x is in meters. The values of the constants are A= 7.95, and B=-7.4

What are the correct units for constant B?

Transcript text: Problem 10: ( $10 \%$ of Assignment Value) A particle's velocity in meters per second along the $x$-axis is described by $v(x)=A x+B x^{2}$, where the position $x$ is in meters. The values of the constants are $A=$ 7.95 , and $B=-7.4$ What are the correct units for constant $B$ ?

Solution

Solution Steps

Step 1: Identify the Given Information

We are given the velocity function of a particle along the $ x $-axis: \[ v(x) = A x + B x^2 \] where $ A = 7.95 $ and $ B = -7.4 $.

Step 2: Determine the Units of $ B $

To find the units of $ B $, we need to ensure that the units on both sides of the equation match. The left side of the equation, $ v(x) $, has units of meters per second (m/s).

Step 3: Analyze the Units of Each Term

The term $ A x $ must have units of m/s.
- $ A $ has units of m/s divided by meters (m), which simplifies to 1/s.
The term $ B x^2 $ must also have units of m/s.
- $ B $ must have units of m/s divided by $ x^2 $ (m$^2$), which simplifies to 1/(m·s).