A bus begin to move with an acceleration of 1 m/s2. A man who is 48 m behind the bus starts running at 10 m/s to catch the bus. The man will be able to catch the bus after.
For bus:
Using the second equation of motion: s = ut + at2
where: s1 = distance covered = ? m
u = initial velocity = 0 m/s
a = acceleration = 1 m/s2
t = time = ts
s1 = ut + at2
s1 = 0 × t + × 1 × t2 = t2/2
Distance travelled by the man, s2 = 10t
s2 – s1 = 48 m
10t - t2/2 = 48
20t – t2 = 96
20t – t2 – 96 = 0
t2 – 20t +96 =0
(t-12)(t-8) = 0
t = 12s or 8s