Question

1) A train starting from a railway station & moving with uniform acceleration, attains a speed of 40km/h in 10m. Its acceleration is?
2) A body starts falling from height 'h' & travels distance h/2 during the last second of motion.The time of travel ?(in sec)

Answer 1

1.
initial velocity, u = 0
final velocity, v = 40 km/h = 11.11 m/s
displacement, s = 10 m
acceleration = a

v² - u² = 2×a×s
⇒11.11² - 0 = 2a×10
⇒20a = 123.43
⇒ a = 6.17 m/s²

2.
u=0
let total time of travel = t

Since it travels h/2 in last 1 second, the first h/2 is travelled in (t-1)second.
h/2 = (1/2)×g×(t-1)²
⇒h = g×(t-1)²

also h = (1/2)×g×(t)²

from both equations
(1/2)×g×(t)² = g×(t-1)²
⇒t²/2 = (t-1)²
⇒t²/2 = t² - 2t + 1
⇒t²/2 -2t + 1 = 0
By solving, we get
t = 3.414s (0.59s is not possible as it is less than 1 second)