Question

A car travels with a velocity of 5 ms. It then accelerates uniformly and travels a distance of 50 m. If the velocity reached is 15 ms ', find the acceleration and the time to travel this distance.​ please answer this question in a good way​

Answer 1

$\Large{\underline{\sf{Required \; Answer :}}}$

As per the provided information in the given question, we have :

• Initial velocity, u = 5 m/s
• Distance covered, s = 50 m
• Final velocity, v = 15 m/s

We have to find the acceleration and time taken.

By using the 3rd equation of motion,

➛ v² — u² = 2as

• v denotes final velocity
• u denotes initial velocity
• a denotes acceleration
• s denotes distance

➛ (15)² – (5)² = 2 × a × 50

➛ 225 – 25 = 100a

➛ 200 = 100a

➛ 200 ÷ 100 = a

➛ 2 m/s² = a (Answer)

Now, by using the 1st equation of motion,

➛ v = u + at

• v denotes final velocity
• u denotes initial velocity
• a denotes acceleration
• t denotes time

➛ 15 = 5 + 2t

➛ 15 – 5 = 2t

➛ 10 = 2t

➛ 10 ÷ 2 = t

➛ 5 seconds = t (Answer)

Therefore, acceleration of the car is 2 m/s² and time taken by the car is 5 seconds.

Answer 2

Note :- I don't wanna to copy that mod answer. So I have used other method

Given :-

A car travels with a velocity of 5 ms. It then accelerates uniformly and travels a distance of 50 m. If the velocity reached is 15 ms ',

To Find :-

Acceleration

Time

Solution :-

We know that

${\large{\boxed{\underline{\underline{{\textsf{\textbf{\color{maroon} v = u + at }}}}}}}}$

$\rm : \implies \: 15 = 5 + at$

$\rm : \implies \: 15 - 5 = at$

$\rm : \implies \: 10 = at$

$\rm : \implies \dfrac{10}{a} = t \: \: (..1)$

Now

By using 2nd equation of Kinematics

${\large{\boxed{\underline{\bf s=ut+\dfrac{1}{2}at^2}}}}$

$\rm : \implies50 = 5 \times \dfrac{10}{a} + \dfrac{1}{2} \times a \times {\bigg( \dfrac{10}{a} \bigg) }^{2}$

$\rm : \implies \: 50 = \dfrac{50}{a} + \dfrac{1}{2} \times a \times \dfrac{100}{ {a}^{2} }$

$\rm : \implies \: 50 = \dfrac{50}{a} + \dfrac{50}{a}$

$\rm : \implies \: 50 = \dfrac{50 + 50}{a}$

$\rm : \implies \: 50 = \dfrac{100}{a}$

$\rm : \implies \: 50a = 100$

$\rm : \implies \: a = \dfrac{100}{50}$

$\rm : \implies \: a = 2 \: ms {}^{ - 2}$

From 1

$\rm : \implies \dfrac{10}{a} = t$

$\rm : \implies \dfrac{10}{2} = t$

$\rm : \implies \: 5 = t$

Therefore,

Time taken is 5 s & acceleration is 2 m/s²