A man is 50 m behind a bus, both at rest. Now, the bus begins to move with constant velocity of 5 m/s. The man runs after the bus to catch it with constant acceleration of 2 m/s2. Then select correct statement
a)Distance covered by the bus till the man catches it is 80 m
b)Time taken by the man to catch the bus is 16 s
c)Distance covered by the man during running is 100 m
d)Speed of man at the moment he catches the bhs is 20 m/s
Answers
Given info : A man is 50 m behind a bus, both at rest. Now, the bus begins to move with constant velocity of 5 m/s. The man runs after the bus to catch it with constant acceleration of 2 m/s².
we have to select the correct statement among given statements.
solution : let after time t, man catches the bus.
distance covered by the bus = s₀ + ut = 50 + 5m/s * t = 50 + 5t [ s₀ is initial position of bus with respect to man]
and the distance covered by the man = 1/2at² = 1/2 *2*t² = t²
to catch the bus, 50 + 5t = t² ⇒ t = 10 sec
∴ time taken by the man to catch the bus is 10 sec.
then distance covered by the bus till the man catches it = 5t = 5 × 10 = 50 sec.
distance covered by the man during running = t² = (10)² = 100m
speed of the man at the moment, he catches the bus = at = 2 × 10 = 20m/s
from above explanation, it is clear that options (c) and (d) both are correct.