Question

An 8 kg block is pushed across a horizontal surface by a horizontally oriented force whose magnitude varies in time. The instantaneous power supplied by the pushing force to the block is P subscript p u s h end subscript open parentheses t close parentheses equals open parentheses 4 straight W over straight s cubed close parentheses t cubed If the block starts at rest at t = 0 s, what is the displacement (in m) of the block after 3 s?

Answer 1

Answer:

4.5 m

Explanation:

We are given that

Mass of block,m=8 kg

$P_push(t)=(4\frac{W}{s^3})t^3$

Apply work energy theorem

$Wdt=d(K.E)$

Where $W=4t^3$

Integrating on both sides

$\int_{0}^{t} 4t^3dt=\int d(K.E)$

$K.E=t^4$

$v=\sqrt{\frac{2K.E}{m}}$

$v=\sqrt{\frac{2t^4}{8}}=\frac{t^2}{2}$

$\frac{ds}{dt}=\frac{t^2}{2}$

$ds=\frac{1}{2}t^2dt$

integrating on both sides

$s=\int_{0}^{t}\frac{1}{2}t^2 dt$

$s=\frac{1}{6}t^3$

Substitute t=3 s

$s=\frac{1}{6}(3)^3=4.5 m$

Hence, the displacement of the block after 3 s=4.5 m