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

Question

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

Badiuddin askIITians.ismu Expert · Answer

Dear abhingya d 2 s/dt 2 =bt intigrate V= ds/dt = bt 2 /2 +c at t=0 V=U so U =0 +c ds/dt = bt 2 /2 +U furthet intigrate s= b/6 t 3 +Ut +d at t=0 s=0 so d=0 S =b/6 t 3 +Ut Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE & AIEEE preparation. All the best. Regards, Askiitians Experts Badiuddin

Mukunda Nagre · Answer

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

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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)bt 2 b) ut+(1/2)bt 2 c) ut+(1/6)bt 3 d) ut+(1/3)bt 3

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

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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)bt 2 b) ut+(1/2)bt 2 c) ut+(1/6)bt 3 d) ut+(1/3)bt 3

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

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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