Question

A car travelling at 50m/s from rest covers a distance of 10km in 40min.calculate the the acceleration.

Answer 1

$\huge{\underline{\underline{\red{\mathfrak{AnSwEr :}}}}}$

$\rule{200}{1}$

$\small{\underline{\blue{\sf{Given :}}}}$

• Final Velocity (v) = 50 m/s
• Final Velocity (u) = 0 m/s
• Distance (s) = 10 km = 1000 m
• Time (T) = 40 mins

$\small{\underline{\green{\sf{Solution :}}}}$

$\sf{Use\; Formula :} \\\\\ \large \star {\boxed{\sf{v^2 \; - \; u^2 \; = \; 2as}}}$

$\implies {\sf{(50)^2 \; - \; (0)^2 \; = \; 2(a)(100)}} \\\\ \implies {\sf{2500 \; - \; 0 \; = \; 200a}}$

$\implies {\sf{2500 \; = \; 200a}}\\\\ \implies {\sf{a \; = \; \dfrac{2500}{200}}}$

$\implies {\sf{a \; = \; 12.5}} \\\\ \implies {\boxed{\sf{Acceleration (a) \; = \; 12.5 \; ms^{-2}}}}$

${\mathbf{\therefore \; Acceleration \; is \; 12.5 \; ms^{-2}}}$

Answer 2

$\bf{\huge{\underline{\sf{\bigstar\:{Correct\:Question\::}}}}}$

A car travelling at 50m/s from rest covers a distance of 10km in 40 seconds.

Calculate the acceleration.

$\bf{\Huge{\boxed{\tt{\green{ANSWER\::}}}}}$

$\bf{Given}\begin{cases}\sf{Final\:Velocity\:of\:a\:Car\:(v)\:\:=50m/s}\\ \sf{Initial\:velocity\:of\:a\:car\:(u)\:=\:0m/s}\\ \sf{Time,[t]\:=\:40seconds}\\ \sf{Distance\:of\:a\:car\:(d)\:\:=10km}\\ \sf{Distance\:of\:a\:car\:\:(d)\:=\:(10*1000)m=10000m}\end{cases}}$

$\bf{\Large{\underline{\bf{To\:Find\::}}}}$

The acceleration.

$\bf{\Large{\underline{\tt{\pink{Explanation\::}}}}}$

Using the second equation of motion are;

$\bf{\Large{\boxed{\sf{S\:=\:ut\:+\:\frac{1}{2} at^{2} }}}}}$

Therefore,

$\implies\sf{10000\:=\:0*40\:+\:\frac{1}{2} *a*(40)^{2} }$

$\implies\sf{10000\:=\:0+\frac{1}{\cancel{2}} *a*\cancel{1600}}$

$\implies\sf{10000\:=\:0+800a}$

$\implies\sf{10000\:=\:800a}$

$\implies\sf{a\:=\:\frac{10000}{800} }$

$\implies\sf{a\:=\:\cancel{\frac{10000}{800}} }$

$\implies\sf{\red{\huge{\boxed{\tt{{a\:=\:12.5m/s}}}}}}$

Thus,

The acceleration (a) is 12.5m/s.