A particle is moving in a straight line such that its velocity varies as `v=v_(0) e^(-lambdat)`, where `lambda` is a constant. Find average velocity during the time interval in which the velocity decreases from `v_(0)` to `v_(0)/2`.

A particle moves in a straight line so that its velocity at any point is given by v^(2)=a+bx , where a,b ne 0 are constants. The acceleration is

A particle in moving in a straight line such that its velocity is given by v=12t-3t^(2) , where v is in m//s and t is in seconds. If at =0, the particle is at the origin, find the velocity at t=3 s .

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 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.

A particle is moving in a straight line such that dv//dt=-lambdav , where v is the velocity and lambda is a constant. At t=0 , the particle is at the origin and moves with velocity v_(0) . Sketch the following graphs: (a) v-t (b) s-t (c ) v-s (d) log_(e)v v//s t

A particle is moving in a straight line. It covers half of the total distance with velocity v_(0) Remaining half distance is covered with a velocity v_(1) for half the time and with velocity v_(2) for another half of time. Find the average velocity of the particle.

A particle is moving in a straight line under constant acceleration alpha. If the intial velocity is v_(0) , sketch the v-t and s-t graphs. (v_(0)gt0) .

A particle is moving in a straight line and its velocity varies with its displacement as v=sqrt(4+4s) m/s. Assume s=0 at t=0. find the displacement of the particle in metres at t=1s.

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