Question

A
A car moning with a speed of 72 lemph, applies
Break for 5 seconds. After 5 seconds, the speed of
(ar 18 kmph Calculate the auleration
the car​

Answer 1

Correct Question :

➥ A car moving with a speed of 72kmph applies brakes for 5 seconds. After 5 seconds, the speed of a car is 18 kmph, Calculate the acceleration of the car.

Answer :

➥ The acceleration of a car = -3 m/s

Given :

➤ Intial velocity of a car = 72 km/hr

➤ Final velocity of a car = 18 km/hr

➤ Time taken by a car = 5 sec

To Find :

➤ Acceleration of a car = ?

Required Solution :

✒ To find the acceleration of a car, first we need to convert the Intial velocity and final velocity km/hr to m/s. To convert multiply the speed by 5/18, then after we will find the acceleration of a car.

◈ Initial velocity = 72

→ Intial velocity = 72 × 5/18

→ Intial velocity = 4 × 5

→ Intial velocity = 20 m/s

◈ Final velocity = 18

→ Final velocity = 18 × 5/18

→ Final velocity = 1 × 5

→ Final velocity = 5 m/s

Now, we have Intial velocity, final velocity, and it's time taken by a car.

• Intial velocity of a car = 20 m/s
• Final velocity of a car = 5 m/s
• Time taken by a car = 5 sec

We can find Acceleration of a car by using the first equation of motion which says v = u + at.

Here,

• v is the final velocity in m/s.
• u is the intial velocity in m/s.
• a is the acceleration in m/s².
• t is the time taken in second.

✎ So let's calculate Acceleration (a) !

⇛ v = u + at

⇛ 5 = 20 + a × 5

⇛ 5 = 20 + 5a

⇛ 5 - 20 = 5a

⇛ -15 = 5a

⇛ -15/5 = a

⇛ -3 = a

⇛ a = -3 m/s

║Hence, the acceleration of car is -3 m/s².║

$\:$

Some related equations :

⪼ First equation of motion: v = u + at

⪼ Second equation of motion: s = ut + ½ at²

⪼ Third equation of motion: v² = u² + 2as

Where,

• v is the final velocity in m/s.
• u is the intial velocity in m/s.
• a is the acceleration in m/s².
• t is the time taken second.
• s is the distance in m.

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Answer 2

Answer:

$\tiny\qquad\qquad \qquad \large\dag \: \red{\underline{\tt Given:}}$

• Initial velocity (u) = 72 km/hr

• Final velocity (v) = 18 km/hr

• Time (t) = 5 seconds

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

$\dashrightarrow\:\:\sf Initial \: velocity \: (u)= 72 \: km/hr$

$\dashrightarrow\:\:\sf Initial \: velocity \: (u)= 72\times\dfrac{5}{18} \: m/sec$

$\dashrightarrow\:\:\sf Initial \: velocity \: (u)= 20 \: m/sec$

____________________

$\dashrightarrow\:\:\sf Final \: velocity \: (v)= 18 \: km/hr$

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

$\dashrightarrow\:\:\sf Final \: velocity \: (v)= 5 \: m/sec$

_____________________

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

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

$:\implies\sf Acceleration = \dfrac{5-20}{5}$

$:\implies\sf Acceleration = \dfrac{ - 15}{5}$

$:\implies \underline{ \boxed{\sf Acceleration = -3 \: m/s^{2} }}$

$\therefore\:\underline{\sf{Acceleration \: produced \: is \: -3\: m/s^{2}}}.$