The radius vector of a point depends on time t, as
`r = c t +(b t^(2))/(2)`
where c and b are constant vectors. Find the modulus of velocity and acceleration at any time t.

The velocity v of a particle is related to time t as v = 4+2 (c_(1)+c_(2)t) , where c_(1) and c_(2) are constants . Find out the initial velocity and acceleration.

if position vector is vecx = 3t^3+2t^2-t find the value of velocity and acceleration.

A radius vector of a particle varies with time t as r=at(1-alphat) , where a is a constant vector and alpha is a positive factor. Find: (a) the velocity v and the acceleration w of the particles as functions of time, (b) the time interval Deltat taken by the particle to return to the initial points, and the distance s covered during that time.

if position vector is vecr =t^3−6t^2+3t+4m find the value of velocity and acceleration.

Displacement (x) of a particle is related to time (t) as x = at + b t^(2) - c t^(3) where a,b and c are constant of the motion. The velocity of the particle when its acceleration is zero is given by:

A radius vector of point A relative to the origin varies with time t as vec r = at hat i - bt^2 hat j where a and b are constant. The equation of point's trajectory is.

A radius vector of point A relative to the origin varies with time t as vec r = at hat i - bt^2 hat j where a and b are constant. The equation of point's trajectory is.