Question

10. A particle travels with an initial velocity of +6.0 m/s and moves with an acceleration of -2.0 m/s
. Calculate the displacement of the particle after 5 seconds?

Answer 1

Given:

• Initial velocity of particle, u = +6 m/s
• Acceleration of particle, a = -2 m/s²
• Time for which it travel, t = 5 sec

To find:

• Displacement of the particle, s =?

Formula required:

• Second equation of motion

      s = u t + 1/2 a t²

[ Where s is displacement, u is initial velocity, t is time taken, a is acceleration ]

Calculation:

Using second equation of motion

→ s = u t + 1/2 a t²

→ s = ( 6 ) ( 5 ) + 1/2 ( -2 ) ( 5 )²

→ s = 30 - ( 5 )²

→ s = 30 - 25

→ s = 5 metres

Therefore,

• Displacement of particle would be 5 metres .

Three equations of motion:

• First equation of motion

       v = u + a t

• Second equation of motion

       s = u t + 1/2 a t²

• Third equation of motion

       2 a s = v² - u²

[ Where v is final velocity, u is initial velocity, a is acceleration, t is time taken and s is displacement ]

Answer 2

Answer:

✡ Given ✡

$\leadsto$ A particle travels with an initial velocity of 6 m/s and moves with an acceleration of -2 m/s.

✡ To Find ✡

$\leadsto$ What is the displacement of the particle after 5 second.

✡ Formula Used ✡

✴ s = ut + $\dfrac{1}{2}$ at² ✴

✡ Solution ✡

Given:-

• u = 6 m/s
• t = 5 second
• a = -2 m/s²

▶ According to the question by using the formula we get,

$\implies$ s = (6).(5) + $\dfrac{1}{2}$ (-2).(5)²

$\implies$ s = (30) - (5)²

$\implies$ s = 30 - 25

$\implies$ s = 5 metres

$\therefore$ The displacement of the particle after 5 second is 5 metres.

______________________

✡ Additional Information ✡

➡ There are three equation of motion :-

⭐ First equation of motion ⭐

$\mapsto$ v = u + at

⭐ Second equation of motion ⭐

$\mapsto$ v² = u² + 2as

⭐ Third equation of motion ⭐

$\mapsto$ s = ut + $\dfrac{1}{2}$ at²

where,

• s = displacement
• u = initial velocity
• v = final velocity
• a = acceleration
• t = time taken

Note:- These equation are reffered as SUVAT equation where SUVAT stands for,

• s = displacement
• u = initial velocity
• v = final velocity
• a = acceleration
• t = time taken

Explanation:

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