A particle moves in such a way that its position vector at any time `t "is" `t "is" hati+`1/2 t^(2) hatj + thatK` Find a function of time (a) the velocity, (b) the speed, (c) the acceleration, (d) the magnitude of the acceleration, (e) the magnitude of the component of acceleration along velocity (called tangential' acceleration), (f) the magnitude of the component ofacceleration 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).

An object moves in such a way that its position (in meters) as a function of time (in seconds) is vecr=hati+3t^(2)hatj+thatk . Give expressions for (a) the velocity of the object and (b) the acceleration of the object as functions of time.

An object is moving in x-y plane its velocity and acceleration at t=0 are represented in figure. The ratio of magnitude of velocity to magnitude of component of acceleration along velocity at t=0 :-

A particle moves in xy plane with its position vector changing with time (t) as vec(r) = (sin t) hati + (cos t) hatj ( in meter) Find the tangential acceleration of the particle as a function of time. Describe the path of the particle.

For a body in circular motion with a constant angular velocity, the magnitude of the average acceleration over a period of half a revolution is how many times the magnitude of its instantaneous acceleration?

For a body in circular motion with a constant angular velocity, the magnitude of the average acceleration over a period of half a revolution is … times the magnitude of its instantaneous acceleration.

Figur shows the total acceleration and velocity of a particle moving clockwise in a circle of radius 2.5m at a given instant of time. At this instant, find: (a) the radius acceleration, (b) the speed of the acceleration, (c) its tangential acceleration.

A particle has initial velocity (2hati+3hatj) and acceleration (0.3hati+0.2hatj) . The magnitude of velocity after 10 second will be

The position vector of an object at any time t is given by 3t^(2) hati +6t hayj +hatk . Its velocity along y-axis has the magnitude

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.