Question

A body starts from rest and with a uniform acceleration of $10\dfrac{m}{{{s^2}}}$ for $5$ second. During the next $10$ second it moves with uniform velocity. The total distance travelled by the body is?

Answer 1

This question is to be solved in the inertial frame of reference. In classical physics and special relativity, an inertial frame of reference is defined as the frame of reference which is not undergoing any acceleration. Newton's equations of motion are applicable to this frame of reference only.

Complete step by step answer:
The initial velocity which is given is $u = 0\dfrac{m}{s}$ (as the body was initially at rest)
The acceleration of the body is $a = 10\dfrac{m}{{{s^2}}}$
The time given is $t = 5s$. On applying the first equation of motion, we get,
$v = u + at$
From this equation, the velocity is
$v = 0 + 10 \times 5$
$\Rightarrow v = 50\dfrac{m}{s}$
The distance travelled by the body in the first $5s$,
On applying the second equation of motion,
$s = ut + \dfrac{1}{2}a{t^2}$
$\Rightarrow s = (0 \times 5) + \left( {\dfrac{1}{2} \times 10 \times {5^2}} \right)$
$\Rightarrow s = 5 \times 5 \times 5$

On further solving,
$s = 125\,m$
So, the distance travelled in the following $10s$ is given by,
${s_1} = v \times {t_1}$
On putting the values, we get,
${s_1} = 50 \times 10$
$\Rightarrow {s_1} = 500\,m$
So, the total distance travelled by the body is
$d = s + {s_1}$
On putting the required values, we get,
$s = 125 + 500$
$\therefore s = 625\,m$

So, the total distance travelled by the body is $s = 625\,m$.

Note: It is important to note that the equations of motion we used in this question are only valid for uniformly accelerated motion. The three equations of motion will not hold good for a non-uniformly accelerated body. This is because, for a non-uniformly accelerated motion we cannot consider the inertial frame of reference and we further know that, for a non-inertial frame of reference Newton's law of motion is not valid.