Problem : A body moving with constant acceleration travels the distance 3 metre and 8 metre respectively in one second 2 second. Calculate the 1) initial velocity and 2) the acceleration of body.

Data given:

Distance(s_{1}) = 3m

Time taken (t_{1}) to travel 3 m =1 second

Distance(s_{2}) = 8m

Time taken (t_{2}) to travel 8 m =2 second

Initial velocity (u)= ?

Acceleration (a) = ?

Case 1:

We know

s = ut + 1/2 a. t^{2}

Or s_{1} = ut_{1} + 1/2 a. t_{1}^{2}

or 3 = u . 1 + 1/2 .a . 1^{2}

or 3 = u + a/2 ——-Eqn. 1

Case 2:

s_{2} = ut_{2} + 1/2 a. t_{2}^{2}

or 8 = u . 2 + 1/2 .a . 2^{2}

or 8 = 2u + 2a

or 8/2 = (2u + 2a)/2

or 4 = u + a ——-Eqn. 2

Subracting Eqn. 1 from Eqn. 2 (Eqn. 2 – Eqn. 1) We have:

4 – 3 = (u + a) – (u + a/2)

Or 1 = u + a – u – a/2

Or 1 = a – a/2

Or 1 = (2a – a)/2

Or 1 = a /2

Or a = 2 m/s^{2}

Putting the value of a in Eqn. 1 we have:

3 = u + 2/2

3 = u + 1

Or u = 3 – 1

Or u = 2 m/s

∴ Initial velocity (u)= 2 m/s

Acceleration (a) = 2 m/s^{2} __Answer__

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