Instantaneous velocity of an object varies with time as `v = alpha - beta t^(2)`. Find its position and acceleration as a function of time, also find the object's maximum positive displacement from the origin.

The position x of a particle varies with time t according to the relation x=t^3+3t^2+2t . Find the velocity and acceleration as functions of time.

The velocity v of moving object varies with displacement u as v=3x^(2)-2 ,then the acceleration at x=2m is

The position of a particle varies with function of time as y=(4sin t+3cos t)m . Then the maximum displacement of the particle from origin will be

The velocity of an object varies as v=h(t^(2))/(4) . Calculate the change in position of the ball is time t.

Acceleration of particle moving along the x-axis varies according to the law a=-2v , where a is in m//s^(2) and v is in m//s . At the instant t=0 , the particle passes the origin with a velocity of 2 m//s moving in the positive x-direction. (a) Find its velocity v as function of time t. (b) Find its position x as function of time t. (c) Find its velocity v as function of its position coordinates. (d) find the maximum distance it can go away from the origin. (e) Will it reach the above-mentioned maximum distance?

Draw the velocity-time graph of an object moving with uniform positive acceleration.

A car is moving on a straight road. The velocity of the car varies with time as shown in the figure. Initially (at t=0), the car was at x=0 , where, x is the position of the car at any time 't'. The maximum displacement from the starting position will be :-

The velocity of a particle varies with its displacement as v=(sqrt(9-x^2))ms^-1 . Find the magnitude of the maximum acceleration of the particle.

Particle 's position as a function of time is given by x=-t^(2)+4t+4 find the maximum value of position coordinate of particle.