Question

a particle starts from a point with a velocity of 6m/s and moves with acceleration I f -2m/s².Show that after 6s the particle will be at the starting point

Answer 1

Initial Velocity = 6m/sec

Acceleration = (-2) m/sec²

$\rule{200}{2}$

The particle will be at starting point when the displacement of the particle will be equal to 0.

Hence,

If the particle is at starting point at t=6

Then,

The displacement of the particle must be equal to 0 at t=6

$\rule{200}{2}$

Now,

From 2nd Equation of motion :-

$s = ut + \frac{1}{2}a {t}^{2} \\ \\ \\s = 6 \times 6 + \frac{1}{2}( - 2) \times 36 \\ \\ \\s = 36 + ( - 1)36 \\ \\ \\ \\s = 36 - 36 \\ \\ \\s = 0$

Hence,

The body is at the starting point.

$\rule{200}{2}$

Answer 2

Solution :-

Initial Velocity = 6 m/sec

Acceleration = - 2 m/sec²

The particle will be at starting point when the displacement of the particle will be equal to 0.

Hence,

If the particle is at starting point, t = 6

Then,

The displacement of the particle must be equal to 0, t = 6

Now,

From Second Equation of Motion,

s = ut + 1 / 2 at²

= 6 × 6 + 1 / 2 (- 2) × 36

= 36 + (- 1) × 36

= 36 - 36

s = 0

Hence, the body is at starting point.