!A body moving with uniform acceleration travels 84m in first 6sec and 180m in the next 5sec find the initial velocity and the acceleration of the body
Answers
case 1
displacement = 84m
time taken = 6s
u = intial velocity
a = acceleration
s = ut + (at.t)/2
s/t = u + at/2
84/6 = (2u + at)/2
84*2/6 = 2u + 6a
84*2/6 = 2(u + 3a)
84*2 /6*2= u +3a
14 = u +3a
u = 14-3a
case 2
displacement = 180+ 84 = 264
time taken = 11s
s/t = (2u + at)/2
264*2/11 = 2u + 11a
48 = 2(14-3a) + 11a ( substituting from case 1)
48= 28-6a +11a
20= 5a
a = 4 metre per second square
then u = 14- 3*4
= 2 m/s
case 1
displacement = 84m
time taken = 6s
u = intial velocity
a = acceleration
s = ut + (at.t)/2
s/t = u + at/2
84/6 = (2u + at)/2
84*2/6 = 2u + 6a
84*2/6 = 2(u + 3a)
84*2 /6*2= u +3a
14 = u +3a
u = 14-3a
case 2
displacement = 180+ 84 = 264
time taken = 11s
s/t = (2u + at)/2
264*2/11 = 2u + 11a
48 = 2(14-3a) + 11a ( substituting from case 1)
48= 28-6a +11a
20= 5a
a = 4 metre per second square
then u = 14- 3*4
= 2 m/s