Given position as a function of time

$x(t)=3t^2+5$

Mass of the object:

$m=2\text{ kg}$

We need the work done in the first 5 seconds.

Find velocity

Velocity is the time derivative of position:

$v=\frac{dx}{dt}=\frac{d}{dt}(3t^2+5)=6t$

So,

• At $t=0$: $v_i=6(0)=0$
• At $t=5$: $v_f=6(5)=30\text{ m/s}$

Apply work-energy theorem

Work done by the force equals change in kinetic energy:

$W=\Delta K=\frac{1}{2}m(v_f^2-v_i^2)$

Substitute the values:

$W=\frac{1}{2}(2)(30^2-0^2)$

$W=1\times 900=900\text{ J}$

Match with options

$900\text{ J}$

Hence, the correct option is:

D: 900 J