Question

A car travelling at 20km/h speeds up to 60km/h in 6 seconds. What is its acceleration?
A) 1.67 m/s2
B) 1.85 m/s2
C) 1.37 m/s2
D) 2.17 m/s2
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Answer 1

AnswEr

• Given Time = 6 seconds
• Initial Velocity (u) = 20 km/h
• Final Velocity (v) = 60 km/h

To find Acceleration (a) Formula is given as :

⠀⠀⠀

⠀⠀$\star\: \boxed{\sf{\frak{Acceleration = \dfrac{v - u}{t}}}}$

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

Firstly we've to convert Final velocity (v) & Initial Velocity (u) into m/s.⠀⠀⠀

⠀⠀⠀$:\implies\sf Final \ Velocity (v) = 60 km/h \\\\\\:\implies\sf 16. 7 m/s \\\\\\:\implies\sf Initial \ Velocity (u) = 20 km/h \\\\\\:\implies\sf 5.6 \ m/s$

$:\implies\sf Acceleration = \dfrac{ 16. 7 - 5. 6}{6 \: } \\\\\\:\implies\sf \dfrac{\cancel{11.1}}{\cancel{6}} \\\\\\:\implies\boxed{\sf{\frak{\purple{1.85 \: m/s^2}}}}$

⠀${\therefore} \ \underline{\sf{ Acceleration \ is \ 1.85 \: m/s^2.}}$ ⠀⠀⠀⠀⠀

Answer 2

Answer :

$\qquad \qquad \large\dag \: \underline{\tt We \: have:}$

$\bullet\:\:\textsf{Initial velocity (u) = \textbf{20 km/hr}}$

$\bullet\:\:\textsf{Final velocity (v) = \textbf{60 km/hr}}$

$\bullet\:\:\textsf{Time (t) = \textbf{6 seconds}}$

__________________

$\qquad\tiny \dag\: \underline{\tt First \: of \: all \: we \: will \: convert \: all \: the \: given \: units \: of \: km/hr \: in \: m/sec : }$

$\dashrightarrow\:\:\sf Initial \: velocity \: (u)= 20 \: km/hr$

$\dashrightarrow\:\:\sf Initial \: velocity \: (u)= 20\times\dfrac{5}{18} \: m/sec$

$\dashrightarrow\:\:\sf Initial \: velocity \: (u)= \dfrac{50}{9} \: m/sec$

____________________

$\dashrightarrow\:\:\sf Final \: velocity \: (v)= 60 \: km/hr$

$\dashrightarrow\:\:\sf Final \: velocity \: (v)= 60 \times \dfrac{5}{18} \: m/sec$

$\dashrightarrow\:\:\sf Final \: velocity \: (v)= \dfrac{50}{3} \: m/sec$

_____________________

$\bigstar \: \boxed{\boxed{\sf Acceleration = \dfrac{Change \: in \: velocity}{Time \: taken}}} \: \bigstar$

$:\implies\sf Acceleration = \dfrac{Final \: velocity - Initial \: velocity}{Time \: taken}$

$:\implies\sf a = \dfrac{v - u}{t}$

$:\implies\sf Acceleration = \dfrac{\dfrac{50}{3} - \dfrac{50}{9}}{6}$

$:\implies\sf Acceleration = \dfrac{\dfrac{150 - 50}{9}}{6}$

$:\implies\sf Acceleration = \dfrac{\dfrac{100}{9}}{6}$

$:\implies\sf Acceleration = \dfrac{100}{54}$

$:\implies \underline{ \boxed{\sf Acceleration = 1.851 \: m/s^{2} }}$

⠀

$\therefore\:\underline{\textsf{Acceleration produced is \textbf{1.851 m/s ^{2} }}}.$