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The ratio of the numerical values of the average velocity and average speed of a body is always.

Two balls are rolling on a flat surface. One has velocity components m/s and √3m/s along the rectangular axes x and y, respectively and the other has component 2m/s and 2m/s, respectively. If both the balls start moving from the same point, the angle between their directions of motion is

If the velocity of a particle is v=At+Bt2, where A and B are constant, then the distance travelled by it between 1s and 2s is :

A particle moves along a straight line such that its displacement s at any time t is given by s=t3−6t2+3t+4m, t being is seconds. Find the velocity of the particle when the acceleration is zero.

A particle is moving such that s=t3−6t2+18t+9, where s is in meters and t is in meters and t is in seconds. Find the minimum velocity attained by the particle.

The position of a particle moving on the x-axis is given by x=t^(3)+4t^(2)-2t+5 where x is in meter and t is in seconds (i) the velocity of the particle at t=4 s is 78 m//s (ii) the acceleration of the particle at t=4 s is 32 m//s^(2) (iii) the average velocity during the interval t=0 to t=4 s is 30 m//s (iv) the average acceleration during the interval t=0 to t=4 s is 20 m//s^(2)

A particle is moving along positive x direction and experiences a constant acceleration of 4m/s2 in negative x direction. At time t=3 second its velocity was observed to be 10m/s in positive x direction.

(a) Find the distance travelled by the particle in the interval t=0 to t=3s. Also find distance travelled in the interval t=0 to t=7.5s..

(b) Plot the displacement – time graph for the interval t=0 to 7.5s.

Let s(t)=t3−6t2 be the position function of a particle moving along an s-axis, where s is in meters and t is in sec. find the instantaneous acceleration a(t) and show the graph of acceleration versus time.

Suppose that a particle mvoes on a straight line so that is velocity at time t is v(t)=(t^(2)-2t)m//s . (a). Find the displacement of the particle during the time interval 0 le t le 3 (b). Find the distance traveled by the particle during the time interval 0 le t le 3 .

The position of a particle along the x-axis is given by the equation, x=t^(3)-6t^(2)+9t , where t is measured in seconds and x in meters. (a) Find the velocity at time t (b) What is the velocity at t = 2 s, at = t = 4 s? (c) What is the time instant, when particle is at rest?

The position of a particle varies with time according to the relation x=3t2+5t3+7t, where x is in m and t is in s. Find

(i) Displacement during time interval t = 1 s to t = 3 s.

(ii) Average velocity during time interval 0 – 5 s.

(iii) Instantaneous velocity at t = 0 and t = 5 s.

(iv) Average acceleration during time interval 0 – 5 s.

(v) Acceleration at t = 0 and t = 5 s.

A particle moves along x-axis and its acceleration at any time t is a = 2 sin (πt), where t is in seconds and a is in m/s2 . The initial velocity of particle (at time t = 0) is u = 0.

Q. Then the distance travelled (in meters) by the particle from time t = 0 to t = 1 s will be :

A particle moves along x-axis and its acceleration at any time t is a = 2 sin ( pit ), where t is in seconds and a is in m/ s^2 . The initial velocity of particle (at time t = 0) is u = 0. Q. Then the distance travelled (in meters) by the particle from time t = 0 to t = t will be :

A particle moves along x-axis and its acceleration at any time t is a = 2 sin (πt), where t is in seconds and a is in m/s2 . The initial velocity of particle (at time t = 0) is u = 0.

Q. Then the magnitude of displacement (in meters) by the particle from time t = 0 to t = t will be :

A particle moves along a horizontal line such that its position at any time t is given by s(t)=t3−6t2+9t+1, s in meters and t in seconds.

At what time the particle is at rest?