Find the position function of a particle that moves with velocity `v(t)=cospit` along a coordinate line, assuming that the particle has coordinate `s=4` or time t=0.

A particle moves with a velocity v(t)= (1/2)kt^(2) along a straight line . Find the average speed of the particle in a time t.

If a particle is moving the velocity v(t)=cos pi t, along a straight line such that at t=0, s=4, its position function is given by

A particle move with a velocity v=alpha t^(3) along a straight line.The average velocity in time interval t=0 to t=T is

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?

Acceleration of a particle is given by a= 3t^(2)+2t +1 Where t is time . Find (i) its velocity at time t assuming velocity to be 10 m/s at t = 0. (ii) its position at time t assuming that the particle is at origin at t = 0. (iii) What is the average speed of the particle in the duration t = 0 to t = 1s? (iv) What is the average acceleration of the particle in the duration t = 0 to t = 1s?

Find the time t_0 when x-coordinate of the particle is zero.

The velocity of a particle moving in the positive direction of x-axis veries as v=10sqrtx . Assuming that at t=0 , particle was at x=0

The position of particle moving along the x-axis veries with time t as x=6t-t^(2)+4 . Find the time-interval during which the particle is moving along the positive x-direction.

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.

The position of a particle moving along x-axis varies eith time t as x=4t-t^(2)+1 . Find the time interval(s) during which the particle is moving along positive x-direction.