We know ( v = \fracdsdt = 3t^2 ). Integrate:
[ \int ds = \int 3t^2 , dt ] [ s = t^3 + C_2 ]
Use ( a = v \fracdvds = -0.5v ). Cancel ( v ) (assuming ( v \neq 0 )):
Since the particle moves to increasing ( s ) from rest at ( s=1 ), take positive root.
From ( v = \fracdsdt = 20 - 0.5s ). Separate variables:
Rectilinear Motion Problems And Solutions Mathalino Now
We know ( v = \fracdsdt = 3t^2 ). Integrate:
[ \int ds = \int 3t^2 , dt ] [ s = t^3 + C_2 ]
Use ( a = v \fracdvds = -0.5v ). Cancel ( v ) (assuming ( v \neq 0 )):
Since the particle moves to increasing ( s ) from rest at ( s=1 ), take positive root.
From ( v = \fracdsdt = 20 - 0.5s ). Separate variables: