Question

A particle moves along a straight line in such a way
that its acceleration is increasing at the rate of
2 ms-2 Its initial acceleration and velocity were zero,
the velocity of particle at t = 3 s is
(1) 27 m s-1
(2) 9 ms1
(3) 3 ms1
(4) 1m/s​

Answer 1

Answer:

9 m/s

Explanation:

According to the question,

⇒ ( da / dt ) = 2 m/s²

⇒ da = 2 × dt

⇒ da = 2dt

Integrating on both sides we get,

⇒ ∫ da = 2 ∫ dt

⇒ a = 2t  

Now we know that,

⇒ ( dv / dt ) = a

⇒ dv = a × dt

⇒ dv = adt

Integrating on both sides we get,

⇒ ∫ dv = ∫ adt

⇒ ∫ dv = ∫ 2t.dt

⇒ v = 2t²/2 = t²

Hence Velocity of the particle as a function of time is t².

Therefore Velocity of the particle at t = 3 sec is given by,

⇒ v = ( 3 )²

⇒ v = 9 m/s

Hence the velocity of the particle at 3 seconds is 9 m/s.