Question

The displacement of a particle of mass 1kg is described by s=2t+3t square .find the force acting on particle

Answer 1

Given:

• Mass of particle is 1 kg.
• Displacement (s) = 2t + 3t².

To find:

• Force acting on body?

Calculation:

First of all, let's calculate the acceleration of the object :

• Double differentiation of displacement function gives acceleration.

$s = 2t + 3 {t}^{2}$

$\implies \: v = \dfrac{ds}{dt}$

$\implies \: v = \dfrac{d(2t + 3 {t}^{2} )}{dt}$

$\implies \: v = 6t + 2$

$\implies \: a= \dfrac{dv}{dt}$

$\implies \: a= \dfrac{d(6t + 2)}{dt}$

$\implies \: a= 6 \: m {s}^{ - 2}$

Now, force on body :

$F = m \times a$

$\implies \: F = 1 \times 6$

$\implies \: F = 6 \: N$

So, force on particle is 6 N.