Question

A motor cycle is moving with a velocity of 108 km/hr and it takes 5s to stop it after then breakes are applied .Calculate the force exerted by the breaks on the motorcycle if its mass along with the rider is 250kg.​

Answer 1

$\huge \fbox{Answer}$

$\large \underline{\underline{\frak{ \color{red}Given::}}}$

${ \mapsto \sf{ Initial\: velocity(u) \: of \: motor \: cycle=108km/h}}$

$\mapsto \sf{Mass(m) \: of \: rider=250kg}$

${ \mapsto \sf{Time(t) \: to \: change \: in \: velocity=5sec}}$

$\large \underline{\underline{\frak{ \color{blue}To \: find::}}}$

${ \leadsto \sf{Force(F) \: exerted \: to \: change \: in \: velocity.}}$

$\large \underline{\underline{\frak{ \color{plum}Formula \: required::}}}$

$\star{\fbox{Force(F)=mass(m)×acceleration(a)}} \star$

$\star{ \boxed{ \rm{Acceleration (a)= \frac{Final \: velocity(v)-Initial \: velocity(u) }{Time(t)} }}} \star$

$\large \underline{\underline{\frak{ \color{cyan}Concept \: used::}}}$

${ \rightarrow \sf{To \: change \: the \: unit \: of \: km/h \: to \: m/s \: we \: multiply \:the\: coefficient\:of\:km/h \: to\: \frac{5}{18}. }}$

${ \rightarrow \sf{The \: final \: velocity \: of \: motor \: cycle \: is \: 0m {s}^{ - 1}. }}$

$\large \underline{\underline{\frak{ \color{cya}According \: to \: Question::}}}$

${\implies{\sf{Force(F)=mass(m)×acceleration(a)}} }$

${\implies{\sf{Force(F)=mass(m)×\frac{Final \: velocity(v)-Initial \: velocity(u) }{Time(t)} }}}$

${\implies{\sf{Force(F)=250kg×\frac{0m {s}^{ - 1} -108km {h}^{ - 1} }{5sec} }}}$

${\implies{\sf{Force(F)=250kg×\frac{0m {s}^{ - 1} -(108km {h}^{ - 1} \times \frac{5}{18} )}{5sec} }}}$

${\implies{\sf{Force(F)=250kg×\frac{0m {s}^{ - 1} -30m {s}^{ - 1} }{5sec} }}}$

${\implies{\sf{Force(F)=250kg×\frac{-30m {s}^{ - 1} }{5sec} }}}$

${\implies{\sf{Force(F)=250kg× - 6m {s}^{ - 2} }}}$

${\implies{\sf{Force(F)= - 1500N}}}$

$\bf{Hence,}$

$\: \: \: \: \: \: \: \: \star{\fbox{Force(F)= - 1500N}} \star$

$\bf{Note,}$

$\sf{Opposing \: force \: are \: represented \: by \: negative \: sign.}$

___________________________________________________________

Answer 2

Answer:

Explanation:

Given,

Initial velocity of the motorcycle, u = 108 km/h

Time taken by motorcycle to stop, t = 5 seconds

Final velocity of the motorcycle, v = 0 (As brakes applied)

Mass along with rider, m = 250 kg

To Find,

Force exerted, F = ?

Formula to be used,

Force = Mass × Acceleration

Force = Mass × (v - u)/t

Solution,

Putting all the values, we get

Force = Mass × (v - u)/t

⇒ Force = 250 × (0 - 108 × 5/18)/5

⇒ Force = - 1500 N

Hence, the force exerted by brakes on a motorcycle is - 1500 N.