The unit of [tex]a[/tex] is [tex]\fbox{\begin\\\ \dfrac{m}{s}\\\end{minispace}}[/tex] and unit of [tex]b[/tex] is [tex]\fbox{\begin\\\ \dfrac{m}{s^{2}}\\\end{minispace}}[/tex].
Further explanation:
Concept used:
The units of [tex]at[/tex] and [tex]bt^{2}[/tex] must be equal to the unit of [tex]x[/tex] that is equal to meters.
The addition of term occurs if the units of all the terms are same.
Given:
The position of object is given by the equation [tex]x=at+bt^{2}[/tex].
Calculation:
The unit of term at must be equal to the unit of [tex]x[/tex] that is meters.
To find the unit of [tex]a[/tex] substitute all the units in the equation [tex]x=at[/tex].
[tex]\boxed{\begin{aligned}x&=at\\ \text{meter}&=a\times \text{second}\\a&=\dfrac{\text{meter}}{\text{second}}\end{aligned}}[/tex]
The unit of [tex]bt^{2}[/tex] is also equal to the unit of [tex]x[/tex] that is meters.
[tex]\boxed{\begin{aligned}x&=bt^{2}\\ \text{meter}&=b\times \text{(second)}^{2}\\b&=\dfrac{\text{meter}}{\text{(second)}^{2}}\end{aligned}}[/tex]
Therefore, the unit of [tex]a[/tex] is [tex]\fbox{\begin\\\ \dfrac{m}{s}\\\end{minispace}}[/tex] and the unit of [tex]b[/tex] is [tex]\fbox{\begin\\\ \dfrac{m}{s^{2}}\\\end{minispace}}[/tex].
Learn more:
1. Solution of linear equation ://brainly.com/question/1682776
2. Units and period https://brainly.com/question/558692
3. A problem on congruency https://brainly.com/question/8414067
Answer details:
Grade: High school
Subject: Mathematics
Topic: Units and measurement
Keywords: Equations, units, measurement , meter, second, meter per second, meter per second square, dogs, m\s^2, m\s, position, object, time, velocity.
