The acceleration (a) of an object varies as a function of its velocity (v) as `a=lambda sqrt(v)` where `lambda` is a constant.If at t=0,v=0 ,then the velocity as a function of time (t) is given as `(A) (3)/(4)lambda^(2)t^(3)` `(B) (1)/(4)lambda t` `(C) (1)/(4)lambda^(2)t^(2)` `(D) (1)/(4)lambda^(2)t`

If (tan3A)/(tan A)=lambda then a possible value of (sin3A)/(sin A) is (A) (8)/(3) if lambda=3 (B) 1 if lambda=-1 (C) (1)/(5) if lambda=(-1)/(9) (D) 4 if lambda=2

The acceleration of a particle varies with time t as a=t^(2)+t+2 where t is in seconds. The particle starts with an initial velocity v-3m/s at t=0. find the velocity of the particle at the end of 5s.

The velocity of a particle moving along the xaxis is given by v=v_(0)+lambdax , where v_(0) and lambda are constant. Find the velocity in terms of t.

The velocity of an object moving rectillinearly is given as a functiion of time by v=4t-3t^(2) where v is in m/s and t is in seconds. The average velociy if particle between t=0 to t=2 seconds is

If y=mx+c be a tangent to the hyperbola (x^(2))/(lambda^(2))-(y^(2))/((lambda^(3)+lambda^(2)+lambda)^(2))=1,(lambda!=0), then

If 5cos 2t + 12sin 2t = lambda sin(2t -tan^(-1)mu) where lambda, mu are constants then lambda =____ and mu = ______.

If f(x) is a periodic function with peirodic function with period lambda then f(lambda x + u) where mu is any constant is periodic with period (T)/(a) .

If velocity v varies with time t as v=2t^(2) , then the plot between v and t^(2) will be given as :

Two particle are moving perpendicular to each with de-Broglie wave length lambda_(1) and lambda_(2) . If they collide and stick then the de-Broglie wave length of system after collision is : (A) lambda = (lambda_(1) lambda_(2))/(sqrt(lambda_(1)^(2) + lambda_(2)^(2))) (B) lambda = (lambda_(1))/(sqrt(lambda_(1)^(2) + lambda_(2)^(2))) (C) lambda = (sqrt(lambda_(1)^(2) + lambda_(2)^(2)))/(lambda_(2)) (D) lambda = (lambda_(1) lambda_(2))/(sqrt(lambda_(1) + lambda_(2)))

The velocity of a particle is given by v=v_(0) sin omegat , where v_(0) is constant and omega=2pi//T . Find the average velocity in time interval t=0 to t=T//2.