Question

When a force of (5i+4j) N displaces a particle through (3i-3j). The power is 0.6W. Find the time of action of the force​

Answer 1

Given

When a force of (5i + 4j) N displaces a particle through (3i - 3j) m. The power is 0.6 W

To Find

The time of action of force​

Solution

We know that

$\rm \longrightarrow t=\dfrac{W}{P}$

$\rm \longrightarrow W=F.s$

Equating "W"

We get

$\rm \longrightarrow t=\dfrac{F.s}{P}$

Here

• t = Time
• W = Work done
• F = Force
• s = Distance
• P = Power

Units

• t = second (s)
• W = Joule (J)
• F = Newton (N)
• s = metre (m)
• P = Watt (W)

According to the question

We are asked to find the time of action of force​

Therefore

We must find "t"

Given that

When a force of (5i + 4j) N displaces a particle through (3i - 3j) m. The power is 0.6 W

Hence

• F = (5i + 4j) N
• s = (3i - 3j) m
• P = 0.6 W

Substituting the values

We get

$\rm \longrightarrow t=\dfrac{(5i+4j).(3i-3j)}{0.6} \ s$

$\rm \longrightarrow t=\dfrac{(5 \times 3)-(4 \times 3)}{0.6} \ s$

$\rm \longrightarrow t=\dfrac{15-12}{0.6} \ s$

$\rm \longrightarrow t=\dfrac{3}{0.6} \ s$

$\rm \longrightarrow t=\dfrac{30}{6} \ s$

Therefore

$\rm \longrightarrow t=5 \ s$

Hence

The time of action of force​ = 5 seconds

Answer 2

$\Large\bf{\color{peru}GiVeN,}$

• A force of $\bf{(5\hat{i}\:+\:4\hat{j})\:N}$ displaces a particle through $\bf{(3\hat{i}\:-\:3\hat{j})\:m}$.

$\longmapsto\:\:\bf\blue{Force\:(F)\:=\:(5\hat{i}\:+\:4\hat{j})\:N}$

$\longmapsto\:\:\bf{\color{lime}Displacement\:(s)\:=\:(3\hat{i}\:-\:3\hat{j})\:m}$

• Power (P) = 0.6 W

$\bf{\color{indigo}We\:know\:that,}$

$\red\bigstar\:\:{\pink{\boxed{\boxed{\bf{\color{cyan}Work\:done\:=\:F\:.\:s\:}}}}}---(i)$

$\Large\bf\orange{Or}$

$\purple\bigstar\:\:{\green{\boxed{\boxed{\bf{\color{olive}Work\:done\:=\:Power\times{time}\:}}}}}--(ii)$

$\bf\red{From\:equ^n(i)\:\&\:(ii)\:we\:get,}$

$:\implies\:\:\bf{F\:.\:s\:=\:Power\times{time}\:}$

$:\implies\:\:\bf{Time\:=\:\dfrac{F\:.\:s}{Power}\:}$

$:\implies\:\:\bf{Time\:=\:\dfrac{(5\hat{i}\:+\:4\hat{j})\:.\:(3\hat{i}\:-\:3\hat{j})}{0.6}\:}$

$:\implies\:\:\bf{Time\:=\:\dfrac{15\:(\hat{i}.\hat{i}\:+\:12\:(\hat{j}.\hat{i})\:-\:15\:(\hat{i}.\hat{j})\:-\:12\:(\hat{j}.\hat{j})}{0.6}\:}$

$:\implies\:\:\bf{Time\:=\:\dfrac{15\times{1}\:+\:12\times{0}\:-\:15\times{0}\:-\:12\times{1}}{0.6}\:}$

$:\implies\:\:\bf{Time\:=\:\dfrac{15\:-\:12}{0.6}\:}$

$:\implies\:\:\bf{Time\:=\:\dfrac{3}{0.6}\:}$

$:\implies\:\:\bf{Time\:=\:\dfrac{30}{6}\:}$

$:\implies\:\:\bf\purple{Time\:=\:5\:s\:}$

$\Large\bold\therefore$ The time of action is 5 seconds.