Acceleration of a particle is given by
a =v 
= 
= 
When acceleration is given by a = f(x) then for find velocity in term of x we write a = v 
= f(x) and on
integration we get
= 
But when a is given by a = f(t) then for finding velocity in terms of t we write
= f(t) on integration we get
= 
But when acceleration is given by a = f(v) then we
use 
= f(v) when we have to find v in terms of t and
we used v 
= f(v) when we have to find v in terms of
x.
(i) A particle is moving along a straight line with acceleration a = (2t + 1) and at t = 0, v = 0 the velocity
of the particle is given by –
Text Solution
Verified by ExpertsCHECK THE SOLUTION
Also t 2 = 
where sin α = 
Ans.
(i)
Sol. a = 2t + 1
= 2t + 1
= 
v = t 2 + t
(ii)
Sol. a = 2x + 1
v 
= 2x + 1 ]
= 
= x 2 + x
v 2 = 2(x 2 + x)
v = 
(iii)
Sol. a = (2v + 1)
= 2v + 1
= 
log (2v + 1) = t
log (2v + 1) = 2t
2v + 1 = e 2t ; v = (t 2t –1)/2
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