Question

The velocity of an object with mass = 2kg is given as a function of time:
V = 2ti + 4$t^{2}$j

Find the force acting on the object at t = 2 seconds.

Answer 1

Answer:

The force acting on the object at $t = 2\,s$ is $\vec F = (4, 32)\,[N]$.

Explanation:

Given that object has a constant mass in time, the force acting on the object ($\vec F$), in newtons, is defined by following expression:

$\vec F = m\cdot \vec a$ (1)

Where:

$m$ - Mass, in kilograms.

$\vec a$ - Acceleration, in meters per square second.

By definition of acceleration, we know that:

$\vec a = \frac{d}{dt} \vec v$ (2)

Let suppose that given vector velocity is expressed in meters per second. If we know that $m = 2\,kg$, $\vec v = (2\cdot t, 4\cdot t^{2})\,\left[\frac{m}{s} \right]$ and $t = 2\,s$, then the force acting on the object is:

$\vec a = (2, 8\cdot t)\,\left[\frac{m}{s^{2}} \right]$

$\vec F = (4, 16\cdot t)\,[N]$

$\vec F = (4, 32)\,[N]$

The force acting on the object at $t = 2\,s$ is $\vec F = (4, 32)\,[N]$.