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?

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Solution

$s = 10 t + 4.9 t^{2}$ ...(1)
Acceleration is constant
From kinematics: $s = u t + \frac{1}{2} a t^{2}$ ..(2)
comparing (1) and (2)
i)initial velocity $u = 10 m / s$
ii)Acceleration, $a = 4.9 \times 2 = 9.8 m / s^{2}$
iii) $v^{2} - u^{2} = 2 a s$
$s (t = 3) = 10 \times 3 + \frac{1}{2} \times 9.8 \times 9$
$= 30 + 44.1 = 74.1 m$
$v^{2} = u^{2} + 2 a s$
$= 100 + 2 \times 9.8 \times 74.1 = 1552.36$
velocity at $t = 3, v = 39.4 m / s$

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A particle is moving with a uniform acceleration. Its displacement at any instant t is given by s= 10t +4.9t2. What is (i) initial velocity (ii)velocity at t=3 second and (iii) the uniform acceleration?

s=10t+4.9t2...(1)Acceleration is constantFrom kinematics: s=ut+12at2..(2)comparing (1) and (2)i)initial velocity u=10m/sii)Acceleration,a=4.9×2=9.8m/s2iii)v2−u2=2ass(t=3)=10×3+12×9.8×9=30+44.1=74.1mv2=u2+2as=100+2×9.8×74.1=1552.36velocity at t=3,v=39.4m/s

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?