Question

A motorcar is moving along a straight line with a uniform velocity of 90 km/h. Its velocity is slowed down to 18 km/h in 4 s by an unbalanced external force. Calculate the acceleration.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Acceleration=-5\:m/s^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Initial \: speed(u) = 90 \: km/h \\ \\ \tt: \implies Time(t) = 4 \: sec \\ \\ \tt: \implies Final \: speed(v) = 18 \: km/h \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Acceleration(a) = ?$

• According to given question :

$\tt \circ \: Final \: speed = 18 \times \frac{5}{18} = 5 \: m/s \\ \\ \tt \circ \: Initial \: speed = 90 \times \frac{5}{18} = 25 \: m/s \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies v = u + at \\ \\ \tt: \implies 5 = 25 + a \times 4 \\ \\ \tt: \implies 5 - 25 = a \times 4 \\ \\ \tt: \implies - 20 = a \times 4 \\ \\ \tt: \implies a = \frac{ - 20}{4} \\ \\ \green{\tt: \implies a = - 5 \: m/{s}^{2} } \\ \\ \green{\tt \therefore Acceleration \: of \: motorcar \: is \: - 5 \: {m/s}^{2} } \\ \\ \blue{ \bold{Some \: related \: formula}} \\ \orange{ \tt \circ \: {v}^{2} = {u}^{2} + 2as} \\ \\ \orange{ \tt \circ \: s = ut+ \frac{1}{2}a {t}^{2} }$

Answer 2

Answer:

$:\implies\sf Initial\:Speed\:(u)=90\:km/h\\\\:\implies\sf Initial\:Speed\:(u)=90\times \dfrac{5}{18}\:m/s \\\\:\implies\sf Initial\:Speed\:(u) = 5\times 5 \:m/s\\\\:\implies\sf Initial\:Speed\:(u)= 25 \:m/s \\\\\\\\:\implies \sf Final\:Speed\:(v)=18\:km/h \\\\:\implies \sf Final\:Speed\:(v) =18 \times \dfrac{5}{18}\:m/s \\\\:\implies \sf Final\:Speed\:(v)=5 \:m/s\\\\\\\bullet\sf\:\:Time\:(t)=4\:sec$

$\rule{130}{1}$

$\underline{\bigstar\:\textbf{Using First Equation of Motion :}}$

$\dashrightarrow\sf\:\:v=u+at\\\\\\\dashrightarrow\sf\:\:5\:m/s=25\:m/s +( a \times 4s)\\\\\\\dashrightarrow\sf\:\:5\:m/s - 25\:m/s =(a \times 4s)\\\\\\\dashrightarrow\sf\:\:- \:20\:m/s =(a \times 4s)\\\\\\\dashrightarrow\sf\:\: \dfrac{ - \:20\:m/s}{4s} = a\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf a = -\:5\:m\:s^{-2}}}$

⠀

$\therefore\:\underline{\textsf{Acceleration of motorcar is \textbf{- 5 m s ^{\text{-2}} }}}.$