The pressure of a gas on a piston face of area varies with time according to

MATHEMATICS · Single correct · A Level · Mathematics · Quantities and units in mechanics · Quantities and units in mechanics

Problem

The pressure of a gas on a piston face of area

0.020\,\text{m}^2

varies with time according to

P(t)=\bigl(2.0\times10^{4}t + 1.0\times10^{5}\bigr)\,\text{Pa}

, where

t

is in seconds. What is the average force exerted by the gas on the piston during the interval

0\le t\le 3.0\,\text{s}

? (a)

3.2\times10^{3}\,\text{N}

(b)

2.6\times10^{3}\,\text{N}

(c)

7.8\times10^{3}\,\text{N}

(d)

2.0\times10^{3}\,\text{N}