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).