Question

If m/s, then what is$\left|-\frac{1}{2}\overrightarrow{v}\right|$ ?

Short answer

The value of $\left|-\frac{1}{2}\overrightarrow{v}\right|$is 3.08 m/s .

Step-by-step solution

Understanding the concept of multiplication of vector with a scalar

If a vector is multiplied by a scalar, its corresponding components get multiplied by the scalar individually.The magnitude of a particular vector can be evaluated when its corresponding components are squared and added. Then its square root needs to be found.

Determination of the velocity vector -12v→

The given velocity vector ism/s_.

Multiply the given vector by $-\frac{1}{2}$to get the required velocity vector,

role="math" localid="1653562866807" m/s

m/s

Determination of magnitude of -12v→

Take the square root of sum of the squares of all the components of the vectors to obtain the required magnitude,

$\left|-\frac{1}{2}\overrightarrow{v}\right|=\sqrt{{\left(-1\right)}^2+{\left(\frac{3}{2}\right)}^2+{\left(-\frac{5}{2}\right)}^2}$m/s

role="math" localid="1653562766101" $=\sqrt{1+\frac{9}{4}+\frac{25}{4}}$m/s

$=\sqrt{\frac{4+9+25}{4}}$m/s

= 3.08m/s

Thus, the magnitude of velocity vector is 3.08m/s .