Question

A car traveeling at 20km/hr speeds up to 60km/hr in 6 sec. What is the accelaration

Answer 1

Given :

• Initial velocity of Car, u = 20 km/h
• Final velocity of Car, v = 60 km/h
• time taken for change in velocity, t = 6 sec

To find :

• Acceleration of Car, a =?

Formula required :

• First equation of motion

     v = u  + a t

[ Where v = final velocity, u = initial velocity, a = acceleration, t = time taken ]

Solution :

Converting Initial and final velocity given in km/h to m/s

→ u = 20 km/h

→ u = 20 × 5/18  m/s

→ u = 100/18  m/s

→ u = 50/9  m/s

and

→ v = 60 km/h

→ v = 60 × 5/18  m/s

→ v = 300/18  m/s

→ v = 150/9  m/s

Calculating acceleration of Car

Using first equation of motion

→ v = u + a t

→ 150 / 9 = ( 50 / 9 ) + a ( 6 )

→ 6 a = ( 150 / 9 ) - ( 50 / 9 )

→ 6 a = ( 150 - 50 ) / 9

→ 6 a = 100 / 9

→ a = ( 100 / 9 ) / 6

→ a = 100 / 54

→ a = 1.851  m/s²

Therefore,

• Acceleration of Car is 1.851 m/s².

Answer 2

Answer:

$\tt {\pink{We \: have}}\begin{cases} \sf{\green{Initial \: Velocity \: (u)=20 \: km/hr}}\\ \sf{\blue{Final \: Velocity \: (v)=60 \: km/hr}}\\ \sf{\orange{Time \: taken \: (t)=6 \: sec}}\\ \sf{\red{Acceleration \: (a)= \: ?}}\end{cases}$

$\qquad\tiny \dag \: \underline{\tt Firstly \: we \: have \: to \: convert \: Final \: Velocity(v) \: and \: Initial \: Velocity (u) \: into \: m/s : }$

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

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

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

_____________________

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

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

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

______________________

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

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

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

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

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

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

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