Question

If \[F=\dfrac{mv-mu}{t}\], then u can be written as:
(a) \[\dfrac{mv+Ft}{m}\]
(b) \[\dfrac{mv-Ft}{m}\]
(c) \[\dfrac{v-Ft}{m}\]
(d) \[\dfrac{v+Ft}{m}\]

Answer 1

Hint: In this question, we first need to cross multiply and take the t term to the other side. Then on rearranging the terms we need to keep u term alone one side and the other terms on the other side and then simplify it further.

Complete step-by-step answer:
Equation- A statement of equality of two algebraic expressions involving two or more unknown variables is called equation.
Solution of an Equation- A particular set of values of the variables, which when substituted for the variables in the equation makes the two sides of the equation equal, is called the solution of the equation.
Cross multiplication- In cross multiplication, we multiply the numerator of the first fraction with the denominator of the second fraction and the numerator of the second fraction with the denominator of the first fraction.
Now, from the given equation on cross multiplication we get,
\[\begin{align}
  & \Rightarrow F=\dfrac{mv-mu}{t} \\
 & \Rightarrow Ft=mv-mu \\
\end{align}\]
Let us now rearrange the terms in the above equation.
\[\Rightarrow Ft-mv=-mu\]
Now, on multiplying both sides with -1 we get,
\[\Rightarrow mv-Ft=mu\]
Let us now divide with m on both sides then we get,
\[\therefore u=\dfrac{mv-Ft}{m}\]
Hence, the correct option is (b).

So, the correct answer is “Option (b)”.

Note: Instead of multiplying both the sides with -1 and then later dividing both the sides with m we can directly use the cross multiplication method and then rearrange the terms on the both sides from taking one side to other and then further simplifying it also gives the same result.
It is important to note that at the beginning we need to take the t term to the other side which in turn can also be done as multiplying with t on the both sides. Then while rearranging the terms we need to be careful about the signs after changing them from one side to the other. Because neglecting any one of the signs changes the expression completely.