A particle is moving with uniform acceleration. Its displacement at any instant t is given as $s = 10 t + 49 t^{2}$ . What is the initial velocity, velocity at $t = 3 s e c$ and uniform acceleration?

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Solution

Given:
Acceleration is uniform.
Displacement is given by
$s = 10 t + 49 t^{2}$

According to second equation of motion,
$s = u t + \frac{1}{2} a t^{2}$

On comparing coefficients,
$u t = 10 t \Rightarrow u = 10 m / s$ and
$\frac{1}{2} a t^{2} = 49 t^{2} \Rightarrow a = 2 \times 49 = 98 m / s^{2}$

Velocity at $t = 3 sec$ has be found.
By first equation of motion,
$v = u + a t$
$v = 10 + 98 (3) = 304 m / s$

Thus,
initial velocity $u = 10 m / s$
velocity $v_{t = 3} = 304 m / s$
uniform acceleration $a = 98 m / s^{2}$

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A particle is moving with uniform acceleration. Its displacement at any instant t is given as s=10t+49t2. What is the initial velocity, velocity at t=3 sec and uniform acceleration?

A particle is moving with uniform acceleration. Its displacement at any instant t is given as $s = 10 t + 49 t^{2}$ . What is the initial velocity, velocity at $t = 3 s e c$ and uniform acceleration?