Question

Acar has initial velocity of 72 km h It is accelerated at 2 ms Calculate the final velocity
and the distance covered after 3 seconds. What is the distance covered by the car in 3
second

Answer 1

Aɴsᴡᴇʀ

we have,

initial velocity, u = 72 km/h

first we have to convert the unit of velocity into m/s

$\begin{gathered} \bold{\implies u = \frac{ 72 \times 1 \cancel{000}}{36 \cancel{0 0}} m {s}^{ - 1} } \\ \\ \bold{\implies u = \frac{ \cancel{72} \times 10}{ \cancel{36}} \:m {s}^{ - 1} \: \: \: \: } \\ \\ \bold{ \implies u = 2 \times 10 \: m {s}^{ - 1} \: \: \: \: \: \: \:} \\ \\ \bold{\implies u = 20 \: m {s}^{ - 1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:} \end{gathered}$

_______________________________

so, now we have,

initial velocity, u = 20m/s

acceleration, a = 2 m/s²

time taken, t = 3 sec

final velocity, v = ?

distance, s = ?

now, by first equation of motion :

$\begin{gathered} \boxed{ \red {\bold{at = v - u}}} \\ \end{gathered}$

$\begin{gathered} \bold{ : \implies 2 \times 3=v - 20 } \\ \\ \bold{ : \implies6 = v - 20 } \: \: \: \: \: \: \: \\ \\ \bold{ : \implies \: v = 6 + 20} \: \: \: \: \: \: \: \\ \\ \bold{ : \implies \: \boxed{ \pink {\bold{v = 26 \: m {s}^{ - 1} }}}}\end{gathered}$

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now, by second equation of motion:

$\begin{gathered} \boxed{ \red{\bold{s = ut + \frac{1}{2} a {t}^{2} }}} \\ \end{gathered}$

$\begin{gathered} \bold{ : \implies s =20 \times 3 + \frac{1}{ \cancel{2}} \times \cancel{ 2} \times {3}^{2} } \\ \\ \bold{ : \implies s = 60 + 9} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies \: \boxed{ \pink{\bold{ s = 69 \: m}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{gathered}$

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Hence, final velocity of the car is 26 m/s and distance covered by the car is 69 m

_______________________________

☯︎ important :-

• first equation of motion : at = v - u
• second equation of motion : s = ut + ½ at²
• third equation of motion : v² = u² + 2as

Answer 2

Answer:

Aɴsᴡᴇʀ

we have,

initial velocity, u = 72 km/h

first we have to convert the unit of velocity into m/s

\begin{gathered}\begin{gathered} \bold{\implies u = \frac{ 72 \times 1 \cancel{000}}{36 \cancel{0 0}} m {s}^{ - 1} } \\ \\ \bold{\implies u = \frac{ \cancel{72} \times 10}{ \cancel{36}} \:m {s}^{ - 1} \: \: \: \: } \\ \\ \bold{ \implies u = 2 \times 10 \: m {s}^{ - 1} \: \: \: \: \: \: \:} \\ \\ \bold{\implies u = 20 \: m {s}^{ - 1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:} \end{gathered}\end{gathered}

⟹u=

36

00

72×1

000

ms

−1

⟹u=

36

72

×10

ms

−1

⟹u=2×10ms

−1

⟹u=20ms

−1

_______________________________

so, now we have,

initial velocity, u = 20m/s

acceleration, a = 2 m/s²

time taken, t = 3 sec

final velocity, v = ?

distance, s = ?

now, by first equation of motion :

\begin{gathered}\begin{gathered} \boxed{ \red {\bold{at = v - u}}} \\ \end{gathered}\end{gathered}

at=v−u

\begin{gathered}\begin{gathered} \bold{ : \implies 2 \times 3=v - 20 } \\ \\ \bold{ : \implies6 = v - 20 } \: \: \: \: \: \: \: \\ \\ \bold{ : \implies \: v = 6 + 20} \: \: \: \: \: \: \: \\ \\ \bold{ : \implies \: \boxed{ \pink {\bold{v = 26 \: m {s}^{ - 1} }}}}\end{gathered}\end{gathered}

:⟹2×3=v−20

:⟹6=v−20

:⟹v=6+20

:⟹

v=26ms

−1

_______________________________

now, by second equation of motion:

\begin{gathered}\begin{gathered} \boxed{ \red{\bold{s = ut + \frac{1}{2} a {t}^{2} }}} \\ \end{gathered}\end{gathered}

s=ut+

2

1

at

2

\begin{gathered}\begin{gathered} \bold{ : \implies s =20 \times 3 + \frac{1}{ \cancel{2}} \times \cancel{ 2} \times {3}^{2} } \\ \\ \bold{ : \implies s = 60 + 9} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies \: \boxed{ \pink{\bold{ s = 69 \: m}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{gathered}\end{gathered}

:⟹s=20×3+

2

1

×

2

×3

2

:⟹s=60+9

:⟹

s=69m

_______________________________

Hence, final velocity of the car is 26 m/s and distance covered by the car is 69 m

_______________________________

☯︎ important :-

first equation of motion : at = v - u

second equation of motion : s = ut + ½ at²

third equation of motion : v² = u² + 2as