Question

Acceleration-time graph for a particle is given in
figure. If it starts motion at t = 0, distance travelled
in 3 s will be
(1) 4 m
(2) 2 m
(3) O
(4) 6 m

plz give full solution​

Answer 1

Answer :

Initial velocity of particle is zero.

★ Distance covered in 1st second :

• u = zero
• a = 2 m/s²
• t = 1 s

➝ S(1) = ut + 1/2 at²

➝ S(1) = (0 × 1) + 1/2 (2 × 1²)

➝ S(1) = 0 + 1

➝ S(1) = 1 m

★ Distance covered in 2nd second :

Body moves with constant velocity between t = 1s and t = 2s as it has zero acceleration $.$

Velocity of particle after 1s is given by

• v = u + at
• v = 0 + 2(1)
• v = 2 m/s

➝ S(2) = v × t

➝ S(2) = 2 × 1

➝ S(2) = 2 m

★ Distance covered in 3rd second :

In this case, initial velocity (u) of particle will be 2 m/s.

• u = 2 m/s
• a = -1 m/s²
• t = 1 s

➝ S(3) = ut + 1/2 at²

➝ S(3) = (2 × 1) + 1/2 (-2 × 1²)

➝ S(3) = 2 - 1

➝ S(3) = 1 m

★ Total distance covered by particle :

⭆ S = S(1) + S(2) + S(3)

⭆ S = 1 + 2 + 1

⭆ S = 4 m

∴ (1) is the correct answer!