Question

Sir,
A body moving with a constant acceleration travels the distances 3m and 8m respectively in 1s and 2s. Calculate :(i) the initial velocity and (ii) the acceleration of the body.
How​​ to solve this?

Answer 1

Case 1:

We know

s = ut + 1/2 a. t²
Or s₁ = ut₁ + 1/2 a. t₁²
or 3 = u . 1 + 1/2 .a . 1²
or 3 = u + a/2 -------Eqn. 1

Case 2:

s₂ = ut₂ + 1/2 a. t₂²
or 8 = u . 2 + 1/2 .a . 2²
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/s²
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/s²