A particle is moving with a uniform acceleration. Its displacement at any instant t is given by s= 10t +4.9$t^2$. What is (i) initial velocity (ii)velocity at t=3 second and (iii) the uniform acceleration?

$s=10t+4.9t^2$...(1)

Acceleration is constant

From kinematics: $s=ut+\frac{1}{2}a{t}^2$..(2)

comparing (1) and (2)

i)initial velocity $u=10m/s$

ii)Acceleration,$a=4.9\times 2=9.8m/s^2$

iii)$v^2-u^2=2as$

$s(t=3)=10\times 3+\frac{1}{2}\times 9.8\times 9$

$=30+44.1=74.1m$

$v^2=u^2+2as$

$=100+2\times 9.8\times 74.1=1552.36$

velocity at $t=3,v=39.4m/s$