A particle initially at rest at origin is moving according law 
= 
m/s 2 , where ‘a’ is acceleration.
(i) Velocity of particle at t = 3 sec –
Text Solution
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Ans.
(i)
Sol. a x = 6t a y = 8t
= 6t 
= 8t
∫ dv x = ∫ 6tdt ∫ dv y = ∫ 8tdt
v x = 
= 27 v y = 
= 36
v = 
= 
v = 
= 45 m/s.
| 
| = 10 m/s 2 s = 
at 2 = 
× 10 × 9
= 45 m.
Path straight line.
(ii)
Sol. a x = 6t a y = 8t
= 6t 
= 8t
∫ dv x = ∫ 6tdt ∫ dv y = ∫ 8tdt
v x = 
= 27 v y = 
= 36
v = 
= 
v = 
= 45 m/s.
| 
| = 10 m/s
2 s = 
at 2 = 
× 10 × 9
= 45 m.
Path straight line.
(iii)
Sol. a x = 6t a y = 8t
= 6t 
= 8t
∫ dv x = ∫ 6tdt ∫ dv y = ∫ 8tdt
v x = 
= 27 v y = 
= 36
v = 
= 
v = 
= 45 m/s.
| 
| = 10 m/s
2 s = 
at 2 = 
× 10 × 9
= 45 m.
Path straight line.
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