Question

15. A constant force acts on an object of mass 8kg for a duration of 4 sec. It

increases the object's velocity from 12ms-1 to 48 ms-1 . Find the magnitude of

applied force.​

Answer 1

Answer:

72 N

Explanation:

$\underline{\bigstar\:\textsf{Given:}}$

• Mass (m) = 8 kg
• Time (t) = 4 s
• Initial velocity (u) = 12 m/s
• Final velocity (v) = 48 m/s

$\underline{\bigstar\:\textsf{To\:find:}}$

• Magnitude of force (F) = ?

$\underline{\bigstar\:\textsf{Solution:}}$

By the second law of motion, we comes to know that $\blue{\sf{Force(F)\:=\:mass\:\times\:acceleration(a)}}$

Here, we don't know the acceleration, but we know that $\green{\sf{acceleration\:=\:\dfrac{v\:-\:u}{t}}}$

Here, v = Final velocity

u = Initial velocity

t = time

From this we can find acceleration and then the force applied.

$\:$

$\longmapsto\:\sf{a\:=\:\dfrac{48\:-\:12}{4}}$

$\:$

$\longmapsto\:\sf{a\:=\:\dfrac{36}{4}}$

$\:$

$\longmapsto\:\sf{\underline{\underline{Acceleration\:=\:9\:m/s^2}}}$

$\:$

Now, let's find the force !

$\:$

$\:\::\implies$ F = 8 × 9

$\:$

$\large\:\::\implies\underline{\boxed{\mathrm\purple{Force\:applied\:is\:72\:N}}}$

Answer 2

$\Huge \bf \underline{\underline{Answer:}}$

$\Large \bf{Given}$

$\implies \sf{Mass(m)=8kg}$

$\implies \sf{Initial \: velocity(u)=12m {s}^{ - 1} }$

$\implies \sf{Final \: velocity(v)=48m {s}^{ - 1} }$

$\implies \sf{Time(t)=4sec}$

$\Large \bf{To \: find}$

$\leadsto \sf{Force \: applied \: on \: object.}$

$\Large \bf{Formula \: used}$

$\boxed {\longmapsto{ \bf{Force(F)=Mass(m)×Acceleration(a)}}}$

$\boxed {\longmapsto{ \bf{Acceleration(a)= \frac{Final \: velocity(v)-Initial \: velocity(u)}{Time(t)}\:\:\:[ by\:second\:equation\:of\:motion] }}}$

$\Large \bf{Concept \: used}$

$\sf{Here,we \: doesn't \: know \: acceleration \: of \: object \: so, }$

$\sf{first \: we \: find \: acceleration \: of \: object.}$

$\Large \bf{According \: to \: Question}$

$\bf{ \longrightarrow{Acceleration(a)= \frac{Final \: velocity(v)-Initial \: velocity(u)}{Time(t)} }}$

$\sf{ \longrightarrow{Acceleration(a)= \frac{48 - 12}{4} = \frac{36}{4} m / {s}^{2} = 9m/ {s}^{2} }}$

$\sf{ \longrightarrow{Force(F)=Mass(m)×Acceleration(a)}}$

$\sf{ \longrightarrow{Force(F) = 8kg×9m/ {s}^{2} }}$

$\sf{ \longrightarrow{Force(F) = 72N}}$

________________________________________________________________________________