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Abhingya Patra Grade: 11
        

The acceleration of a particle is increasing linearly with time t as bt. The particle starts from origin with initial velocity u. The distance travelled by the particle in time t will be:


a) ut+(1/3)bt2


b) ut+(1/2)bt2


c) ut+(1/6)bt3


d) ut+(1/3)bt3


 

7 years ago

Answers : (2)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear abhingya


d2s/dt2 =bt


intigrate


V= ds/dt = bt2/2 +c


at t=0 V=U


so U =0 +c


ds/dt = bt2/2 +U


furthet intigrate


s= b/6 t3 +Ut +d


at t=0 s=0


so d=0


S =b/6 t3 +Ut


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Badiuddin

7 years ago
Mukunda Nagre
21 Points
										We have to assume acceration =0 when t=0. So we have the equation: a = bt Since a = dv/dt dv/dt = bt Integrating gives: v = (b/2)t² + C When t=0, v = u, so C = u v = (b/2)t² + uSince v = ds/dt ds/dt = (b/2)t² + uIntegrating gives: s = (b/6)t³ + u.t + K When t=0, s=0, so K=0 s= (b/6)t³ + u.t
										
2 months ago
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