Correct Answer - Option 2 : b + 2c
CONCEPT:
-
Newton’s Second Law of Motion: The rate of change of linear momentum of a body is directly proportional to the external force applied on the body and this change takes place always in the direction of the applied force.
- According to the second law of motion, force
\(Force \propto \frac{{change\;in\;momentum}}{{time}}\)
\(⇒ F = K\frac{{{p_2} - {p_1}}}{t} = K\frac{{m\left( {v - u} \right)}}{t} = Kma\) \(\left[ {\therefore \frac{{v - u}}{t} = a} \right]\)
Where, K = constant of proportionality, p = momentum of the body, m = mass of the body, u = initial velocity of the body, v = final velocity of the body, and a = acceleration of the body.
EXPLANATION:
Given that:
momentum (p) = ct2 + bt + a
- According to the second law of motion, force
\(⇒ F =\frac{dp}{dt}\)
\(⇒ F = \frac{d(ct^2 \; + \; bt \; +\; a)}{dt}\)
⇒ F = 2ct + b
The force on the particle at t = 1 sec is
⇒ F = 2c × 1 + b = b + 2c
- Therefore option 2 is correct.
