A particle moving along x-axis has acceleration f, at time t, given by f = f 0 
, where f 0 and T are constants. The particle at t = 0 has zero velocity, the instant when f = 0, the particle's velocity (v x ) will be:
f 0 T 2
f 0 T
Text Solution
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Acceleration
f = f 0 
or f = 
= f 0 
or dv = f 0 
dt … (i)
Integrating Eq. (i) on both sides,
= 
dt
∴ v = f 0 t – 
. 
+ C … (ii)
where C is constant of integration.
Now, when t = 0, v = 0.
similarly from Eq.(ii), we get C = 0
∴ v = f 0 t – 
. 
…(iii)
As f = f 0 
when f = 0, 0 = f 0 
Substituting, t = T in Eq. (iii), then velocity
v x = f 0 T – 
. 
= f 0 T – 
= 
f 0 T
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