Question

In the equation of motion, $S = ut + \dfrac{1}{2}a{t^2}$, S stands for
A. Displacement in t seconds
B. Maximum height reached
C. Displacement in the tth second
D. None of these

Answer 1

In Newtonian mechanics, we determine the displacement, velocity, acceleration and time using four kinematic equations. The given equation is one of the kinematic equations. Put the units of the quantities in the left hand side of the equation and see what will be the resultant unit of the term represented by S.

Complete answer:
We have four kinematic equations that determine the motion of the body. We can calculate the position, velocity and time of the body using these equations. The equation given in the question is the third kinematic equation.

The given kinematic equation is, $S = ut + \dfrac{1}{2}a{t^2}$. Here, S is the displacement of the body, u is the initial velocity, a is the acceleration and t is the time. If the initial velocity is in m/s, acceleration is in $m/{s^2}$ and time is in seconds, then we can determine the displacement of the body in t seconds. Therefore, the option A is correct.

The given kinematic equation $S = ut + \dfrac{1}{2}a{t^2}$ does not represent the maximum height reached by the body. We can derive the formula for the maximum height using the kinematic equation, ${v^2} = {u^2} + 2as$ in the vertical direction. Therefore, the option (B) is incorrect.

We know the formula for distance covered by the body in nth second is given as,
${S_n} = u + \dfrac{1}{2}a\left( {2n - 1} \right)$
Here, n is the tth second.
Therefore, the option D is incorrect.

So, the correct answer is option A.

Note: Displacement in the tth second is derived using the formula that given in the question. The equation given in the question is only applicable for only objects of relatively greater size. We cannot apply this equation to determine the displacement of the relativistic particles such as photon, electrons.