Question

An object starting from rest travels 20m in first 2s and 150m in the next 4s. What will be the velocity after 7s from the start ?

Answer 1

For first 2s
S = 0.5at^2
20 = 0.5a*4
a = 10m/s^2

v = u + at
v = 0 + 10*2
v = 20m/s


For next 4s
S = ut + 0.5at^2
150 = 20*4 + 0.5*a*16
150 = 80 + 8a
70 = 8a
a = 70/8 m/s^2

It’s acceleration in first 2s is 10m/s^2 and in next 4s is 70/8m/s^2. It is moving in non-uniform acceleration. Hence it is impossible to predict the velocity after next one second (i.e 7s from start).
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If I assume you did typo while writing question and wrote 150m instead of 160m then,
It’s acceleration in next 4s is 80/8 = 10m/s^2. Now it is clear that it’s moving in uniform acceleration of 10m/s^2

After 7s
v = u + at
v = 0 + 10*7
v = 70m/s

It’s velocity after 7s from start is 70m/s, only if it is 160m in question instead of 150m.

Answer 2

s=ut+1/2at²
20=0+1/2 a *4
20=2a
a=10m/s²

v-u=at
x-0=10*7
x=70m/s