Question

The acceleration a of a particle starting from rest

varies with time according to relation

a t .

The velocity of the particle after a time t will ​

Answer 1

Given :-

u = 0

a = αt + β

To find :-

the velocity of the partical after a time t will be

Solution :-

a = dv?dt

αt + β = dv/dt

since, partical start from   rest , its initial velocity is zero.

At time t = 0 , velocity = 0

⇒ $= \int\limits^t_0 {v_{0} dv} = \int\limits^v_o {v_{0} {\alpha t + \beta } dt}$

or

$v = \frac{ax^{t} }{2} + b*t$

thank you

Answer 2

Given :-

u = 0

a = αt + β

To find :-

the velocity of the partical after a time t will be

Solution :-

a = dv?dt

αt + β = dv/dt

since, partical start from   rest , its initial velocity is zero.

At time t = 0 , velocity = 0

⇒  $= \int\limits^t_0 {v_{0} dv} = \int\limits^v_0 {v_{0} ( \alpha t + \beta )dt }$

or

$v = \frac{ax^{2} }{2} + b*t$

thank you