Question

A car starts from rest has a constant acceleration of 4 m/s^2. What is the distance travelled by car in first 3s.​

Answer 1

Explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• Initial velocity = 0m/s

• Acceleration = 4m/s²

• Time = 3sec.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The distance traveled by the car.

$\bf{\underline{\underline\green{Solution:-}}}$

According to the third equation of motion:-

$\boxed{ \rm \leadsto s = ut + \frac{1}{2}a {t}^{2} }$

Here:-

• s = distance = ?

• u = initial velocity = 0m/s

(Here:- u = 0 because the car starts from rest)

• t = time = 3 sec

Substituting the values:-

${ \rm \implies s = ut + \dfrac{1}{2}a {t}^{2} }$

${ \rm \implies s = 0 \times 3 + \dfrac{1}{2} \times 4 \times {3}^{2} }$

${ \rm \leadsto s = 0 + \dfrac{1}{2} \times 4 \times 9 }$

$\rm \implies s = \dfrac{36}{2}$

$\rm \implies s = 18$

$\underline{\boxed{\rm \purple{\therefore Distance \: traveled \: = 18m }}}$

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Additional Information:-

The four equations of motion:-

• $\rm v = u + at$

• $\rm s = u t+ \dfrac{1}{2} a {t}^{2}$

• $\rm {v}^{2} = {u}^{2} + 2as$

• $\rm s_{n} = u + \dfrac{a}{2} \big(2n - 1 \big)$

Answer 2

Answer :

➥ Distance travelled by the car = 18 m

Given :

➤ Intial velocity of the car = 0 m/s

➤ Acceleration of the car = 4 m/s²

➤ Time taken by the car = 3 sec

To Find :

➤ Distance travelled by the car = ?

Solution :

Distance travelled by the car

From second equation of motion

$\tt{: \implies s = ut + \dfrac{1}{2} a {t}^{2} }$

$\tt{: \implies s = 0 \times 3 + \dfrac{1}{2} \times 4 \times 3 \times 3 }$

$\tt{: \implies s = 0 + \dfrac{1}{ \cancel{2}} \times \cancel{4} \times 3 \times 3 }$

$\tt{: \implies s = 0 + 1 \times 2 \times 3 \times 3}$

$\tt{: \implies s = 0 + 2 \times 3 \times 3}$

$\tt{: \implies s = 0 + 6 \times 3}$

$\tt{: \implies s = 0 + 18}$

$\tt{: \implies \green{\underline{ \overline{ \boxed{ \purple{ \bf{ \: \: s = 18 \: m \: \: }}}}}}}$

Hence, the final velocity of the bus is 18 m.

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Some releted equations :

⪼ s = ut + ½ at²

⪼ v = u + at

⪼ v² = u² + 2as