A particle moves along the space curve `vec(r)=(t^(2)+t)hat(i)+(3t-2)hat(j)+(2t^(3)-4t^(2))hat(k)`. (t in sec, r in m ) Find at time `t=2` the (a) velocity, (b) acceleration, (c) speed or magnitude of velocity and (d) magnitude of acceleration.

Find the Cartesian form of the equation of the plane vec(r)=(s-2t)hat(i)+(3-t)hat(j)(2s+t)hat(k)

Position vector vec(r) of a particle varies with time t accordin to the law vec(r)=(1/2 t^(2))hat(i)-(4/3t^(1.5))hat(j)+(2t)hat(k) , where r is in meters and t is in seconds. (a) Find suitable expression for its velocity and acceleration as function of time (b) Find magnitude of its displacement and distance traveled in the time interval t=0 to 4 s .

Position vector vec(r) of a particle varies with time t accordin to the law vec(r)=(1/2 t^(2))hat(i)-(4/3t^(3))hat(j)+(2t)hat(k) , where r is in meters and t is in seconds. Find suitable expression for its velocity and acceleration as function of time

Position vector vec(r) of a particle varies with time t accordin to the law vec(r)=(1/2 t^(2))hat(i)-(4/3t^(1.5))hat(j)+(2t)hat(k) , where r is in meters and t is in seconds. Find suitable expression for its velocity and acceleration as function of time.

A particle moves in such a way that its position vector at any time t is vec(r)=that(i)+1/2 t^(2)hat(j)+that(k) . Find as a function of time: (i) The velocity ((dvec(r))/(dt)) (ii) The speed (|(dvec(r))/(dt)|) (iii) The acceleration ((dvec(v))/(dt)) (iv) The magnitude of the acceleration (v) The magnitude of the component of acceleration along velocity (called tangential acceleration) (v) The magnitude of the component of acceleration perpendicular to velocity (called normal acceleration).

A particle moves in such a way that its position vector at any time t is vec(r)=that(i)+1/2 t^(2)hat(j)+that(k) . Find as a function of time: (i) The velocity ((dvec(r))/(dt)) (ii) The speed (|(dvec(r))/(dt)|) (iii) The acceleration ((dvec(v))/(dt)) (iv) The magnitude of the acceleration (v) The magnitude of the component of acceleration along velocity (called tangential acceleration) (v) The magnitude of the component of acceleration perpendicular to velocity (called normal acceleration).