Question

A body is moving with uniform acceleration covers distance of 30m in 5th second and 80m in 8th second. calculate acceleration and initial velocity​

Answer 1

Correct question:-

A body is moving with uniform acceleration covers a distance if 30m in the 5th second and 80m in the 8th second.Caluclate acceleration and initial velocity.

Given:-

•Distance the body covers in the 5th second=30m

•Distance the body covers in the 8th second=80m

To find:-

•Acceleration of the body

•Initial velocity of the body

Solution:-

We know that,distance covered by a body in the nth second is given by:-

=>Sn=u+a/2(2n-1)

When Sn=30m,n=5

=>30=u+a/2(2×5-1)

=>30=u+9a/2

=>30=u+4.5a ----(1)

When Sn=80m,n=8

=>80=u+a/2(2×8-1)

=>80=u+15a/2

=>80=u+7.5a ----(2)

Now,by subtracting eq.1 from eq.2 we get:-

=>80-30=u+7.5a-(u+4.5a)

=>50=u+7.5a-u-4.5a

=>50=3a

=>a=50/3 m/s²

Putting the value of a in eq.1,we get:-

=>30=u+4.5×50/3

=>30=u+75

=>u=30-75

=>u= -45m/s

Here,the -sign,represents that the initial velocity is in the opposite direction.

Thus:-

•Acceleration of the body is 50/3m/s² or 16.67m/s²

•Initial velocity of the body is 45m/s in the opposite direction.