Que: a car moving with uniform acceleration covers 450 m in a 5 second interval, and covers 700 m in the next 5 second interval. the acceleration of the car is (Gate-98)

(a) 7 m/s2
(b) 10 m/s2
(c) 25 m/s2
(d) 50 m/s2

 Ans: (b)
Explanation: Here 
u = initial velocity
v = final velocity
a = acceleration
t = time
s = distance

 using the relation s = ut + 1/2 at2 and v=u + at, for the first 5 second interval,we have
450 = 5u + 25/2 a   ___(i)
v = u + 5a

for the next 5 second interval (v=u + 5a) will be the initial velocity, then
700 = (u + 5a) 5 + 25/2 a  
700 = 5u + 25a + 25/2 a   ___(ii)

From equations (i) and (ii), we get
700-450 = (5u +25a + 25/2 a) – (5u + 25/2 a)
250 = 25a
a = 250/25
a =10 m/s2