1-A body accelerates from rest at 0.2m/s from one fifth of a minute.calculate the distance covered.2-A bus travelling at 15m/s accelerates uniformly at 4m/s.what is the distance covered in 10s.3-A body which is uniformly retarded comes to rest in 5s after travelling a distance of 10m.what is it's initial velocity?.4-if a body moving with a velocity of 3m/s is brought to rest by a constant force after travelling 15m.calculate the retardation.
1. 1/5 minute = 60/5 = 12 seconds
d = (1/2) a t^2 = .5 * 0.2 * 144 = ?
2. d = Vi t + (1/2) a t^2
3. v = Vi + a t
0 = Vi + a t
so a = -Vi/t
d = Vi t + .5 a t^2 = Vi t + .5(-Vi/t) t^2
10 = Vi(5) - .5 Vi(5) = 2.5 Vi
Vi = 10/2.5 = 4
or more easily average speed = Vi/2 = 10/5
so Vi = 20/5 = 4
4. constant acceleration
Vi = 3
v = Vi + a t
0 = 3 + a t so t = -3/a
15 = 3 t + (1/2) a t^2
15 = 3(-3/a) + (1/2) a (9/a^2)
15 = -9 / a + (1/2)(9/a) = -9/2a
30 a =-9