Question

The distance x covered in time t by a body having velocity $v_0$ and having a constant acceleration a is given by $x=v_{0}t+\frac{1}{2}a{t}^2$. This result follows from

• A. Newton's first law
• B. Newton's second law
• C. Newton's third law
• D. none of these

Answer 1

The correct option is B

Newton's second law

Step 1: Given data.

The distance x covered in time t by a body having velocity $v_0$ and having a constant acceleration a is given by $x=v_{0}t+\frac{1}{2}a{t}^2$

Step 2: Explanation.
$x=v_{0}t+\frac{1}{2}a{t}^2$
Now, differentiating the above equation with respect to t, we get

$\frac{dx}{dt}=v_0+at$
But $\frac{dx}{dt}=v$
$\therefore v=v_0+at$
or $a=\frac{v-v_0}{t}\cdots \left(1\right)$

Now, from newton's second law of motion
$F=ma$
Substitute the value of a from equation (1), and we get
$F=m\times \left(\frac{v-v_0}{t}\right)$.

Hence, option (B) is correct.