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Question

If $$x = at + bt^2$$, where $$x$$ is the distance travelled by the body in kilometer while $$t$$ is the time in seconds, then find the units of $$b$$.


Solution

$$x=at+{ bt }^{ 2 }$$
$$x$$ is in meter. $$t$$ is in second.
Applying law of homogenity.
$$b=\dfrac { \left[ x \right]  }{ \left[ { t }^{ 2 } \right]  } $$
$$b=\dfrac { m }{ { s }^{ 2 } } \Rightarrow \boxed { b=m/{ sec }^{ 2 } } $$

Physics

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