Question

(i)a bus starts from rest with an acceleration of 5ms ^{-2} and .a man who is on motor cycle 24 m behind the bus overtakes the bus in 2 s.if motorcycle moves with uniform velocity find his velocity.(ii)a car has uniform acceleration of 4 m/s^2.Find distance it will cover in 10 sec after start.(iii)if a body moves 200 m in first 10 s and 400 m in next 10 s then find the uniform acceleration of the body.please  the anwer in detail

Answer 1

distance travelled by the bus + 24 m
       = distance travelled by the man in the same time duration 2 seconds

u t + 1/2 a t²  + 24 = v t
0 + 1/2 * 5 * 2² + 24 = v * 2
v = 17 m/s  = velocity of motor cycle.
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a = 4 m/s/s    t = 10 sec.  u = 0
s = u t + 1/2 a t * t = 1/2 * 4 * 10* 10 = 200 meters.

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s1 = distance moved in first 10 seconds = u t + 1/2 a t²
     200 = 10 u + 50 a      as t = 10 sec
    =>  u + 5 a = 20  --- (1)

s2 = distance travelled in the first 20 sec. = u * 20 + 1/2 * a * 20²
     =  200 + 400 = 20 u + 200 a
   =>  u + 10 a = 30    == (2)

solving 1 and 2 equations, we get: 
         a = 2 m/sec²      and  u = 10 m/sec