a particle in 1D motion is subjected to an acceleration a = -alpha . t

1.	a particle in 1D motion is subjected to an acceleration a = -alpha . t, where alpha is a positive constant. initial velocity is u at t = 0. the velocity of particle after time t is
Answer» Given: A PARTICLE in 1D motion is SUBJECTED to an ACCELERATION $a=-\alpha t$ where $\alpha$ is a positive constant. To find: Velocity after time t ? Calculation: $\sf \: a = - \alpha t$ $\sf \implies \: \dfrac{dv}{dt} = - \alpha t$ $\sf \implies \: dv = - \alpha \: t \: dt$ $\sf \displaystyle \sf \implies \: \int dv = - \alpha \int t \: dt$ Putting limits: $\sf \displaystyle \sf \implies \: \int_{0}^{v} dv = - \alpha \int_{0}^{t} t \: dt$ $\boxed{\sf \displaystyle \sf \implies v = - \frac{ \alpha {t}^{2} }{2}}$ HOPE It Helps .