A body of mass 2 kg travels according to law x(t)=p t+q t^2+r t^3, where p=3 ms^-1, q=4 ms^-1

step 1 In this question we have given a force vector and it is told that this maintains the velocity of

A body of mass 2 kg travels according to law x(t)=p t+q...

A body of mass $2 \mathrm{~kg}$ travels according to law $x(t)=p t+q t^{2}+r t^{3}$, where $p=3 \mathrm{~ms}^{-1}, q=4 \mathrm{~ms}^{-1}$ and $r=5 \mathrm{~ms}^{-3}$. The force acting on the body at $t=2 \mathrm{~s}$ is [NCFRT Exemplat] (a) $136 \mathrm{~N}$ (b) $134 \mathrm{~N}$ (c) $158 \mathrm{~N}$ (d) $68 \mathrm{~N}$

A body of mass $2 \mathrm{~kg}$ travels according to law $x(t)=p t+q t^{2}+r t^{3}$, where $p=3 \mathrm{~ms}^{-1}, q=4 \mathrm{~ms}^{-1}$ and
$r=5 \mathrm{~ms}^{-3}$. The force acting on the body at $t=2 \mathrm{~s}$ is [NCFRT Exemplat]
(a) $136 \mathrm{~N}$
(b) $134 \mathrm{~N}$
(c) $158 \mathrm{~N}$
(d) $68 \mathrm{~N}$

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Key Concepts

Kinematics

Kinematics is the branch of mechanics that deals with motion without considering its causes. In problems involving time-dependent position functions, kinematics provides the framework to understand how an object's position, velocity, and acceleration change over time.

Differentiation of Position Functions

Differentiation is a mathematical tool used to compute the rates of change of functions. For motion described by a time-dependent position function, the velocity is the first derivative of position with respect to time, and the acceleration is the second derivative. This process is essential in converting a position-time relation into useful information about an object's motion.

Newton’s Second Law

Newton's Second Law states that the net force acting on a mass is equal to the mass multiplied by its acceleration (F = ma). This principle links kinematics and dynamics by allowing the determination of the force from the acceleration obtained through differentiation of the position function.

Polynomial Motion Equations

Polynomial motion equations are commonly used to model various types of motion where acceleration is not constant. Analyzing these equations involves computing derivatives term-by-term, which is a key technique for obtaining velocity and acceleration in systems described by polynomial functions.

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