Referring to a - x graph, find the velocity when the displacement of the particle is 100 m. assume initial velocity as zero.
Equation of line we get
(a-3) =6−3150−50+(x−50)
a = 3100x+32
Now
a = v dvdx⇒vdvdx=3100x+23
∫v0vdv=∫1000(3100x+32)dx
Limits are given in question itself
At x = 0 v = 0
At x = 100 m v = ?
After integrating
v22]v0=3x2200+3x2]1000
v22=3002+3002=300
v2=600
v = ± 10 √6
Since acceleration is increasing with x
So will the velocity.
So v = 10 √6 m/s