Question

$\large\underbrace{\bf{Question}}$

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.

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Answer 1

Answer:

Given :-

• A car travels with a velocity of 5 m/s.
• It then accelerates uniformly and travels a distance of 50 m.
• The velocity reached is 15 m/s.

To Find :-

• What is the acceleration and the time taken to travel this distance.

Solution :-

First, we have to find the acceleration :

Given :

• Initial Velocity = 5 m/s
• Distance Travelled = 50 m
• Final Velocity = 15 m/s

According to the question by using the formula we get,

$\clubsuit$ Third Equation Of Motion Formula :

$\implies \sf\boxed{\bold{v^2 =\: u^2 + 2as}}$

where,

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• s = Distance Travelled

So, by putting those values we get,

$\implies \bf v^2 =\: u^2 + 2as$

$\implies \sf (15)^2 =\: (5)^2 + 2 \times a \times 50$

$\implies \sf (15 \times 15) =\: (5 \times 5) \times 2a \times 50$

$\implies \sf 225 =\: 25 \times 100a$

$\implies \sf 225 - 25 =\: 100a$

$\implies \sf 200 =\: 100a$

$\implies \sf \dfrac{200}{100} =\: a$

$\implies \sf 2 =\: a$

$\implies \sf\bold{\underline{a =\: 2\: m/s^2}}$

Hence, the acceleration is 2 m/s² .

Now, we have to find the time taken to travel this distance :

Given :

• Final Velocity = 15 m/s
• Initial Velocity = 5 m/s
• Acceleration = 2 m/s²

According to the question by using the formula we get,

$\clubsuit$ First Equation Of Motion Formula :

$\implies \sf\boxed{\bold{v =\: u + at}}$

where,

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• t = Time Taken

So, by putting those values we get,

$\implies \bf v =\: u + at$

$\implies \sf 15 =\: 5 + 2t$

$\implies \sf 15 - 5 =\: 2t$

$\implies \sf 10 =\: 2t$

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

$\implies \sf 5 =\: t$

$\implies \sf\bold{\underline{t =\: 5\: seconds}}$

$\therefore$ The acceleration is 2 m/s² and the time taken to travel this distance is 5 seconds .

Answer 2

Answer:

Initial Velocity (u) = 10 m/sec

$Acceleration (a) = 5 m/sec {}^{2}$

Distance (s) = 30 m

Final velocity (v) = ??

Using Newton's Third law of Motion,

$v {}^{2} =u+ {}^{2} as$

$v {}^{2} =10 {}^{2} +2×5×30$

$v {}^{2} =100+300$

$v {}^{2} =400$

$v = \: \: \: \: \: \: \: \: \: \: \: \: \: \\ 400$

$v = 20 m/sec$

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ANSWER =

FINAL VELOCITY = 20 m/sec