Question

A particle experiences a constant acceleration for 12 second after starting from rest. If it travels a distance s1 in the first four second, s2 in the next four second and a distance s3 in last four second, then which of the following options is correct?

s1 : s2 : s3 = 1 : 4 : 9
s1 : s2 : s3 = 1 : 3 : 5
s1 : s2 : s3 = 3 : 4 : 5
s1 : s2 : s3 = 1 : 2 : 3

If a particle is falling freely under gravity from a large height, then
Its velocity always increases
Its velocity always decreases
Its velocity may increase or decrease
Its velocity remains constant

Answer 1

The last option is correct

ΔT1 = 4 sec ΔT2 = 4 sec ΔT3 = 4 sec

S = V0 t + 1/2 a t^2

S1 = 1/2 a t^2 = 8 a where V0 is the speed at the start of the interval

During any interval (of 4 sec) the particle travels 1/2 a t^2 = 8 a due to its acceleration - and you need to include the speed at the start of the interval

S1 = 8a

S2 = 8 a + 8 a = 16 a

S3 = 16 a + 8 a = 24 a

Note: V2 = V1 + a t for any interval

V2 - V1 = V1 + a t - V1 = a t

and a = (V2 - V1) / t = a the speed increase is constant during the interval