Q. 84.3( 6 Votes )
The velocity of a particle moving in the positive direction of X-axis varies as v = a√x where ‘a’ is positive constant. Assuming that at the moment t = 0 the particle was located at x = 0 the value of time dependence of the velocity and acceleration of the particle.
Given: at t = 0 and x = 0 ..1
Putting 1 in 2, we get:
Integrating both sides:
At t = 0, x = 0 so c = 0 ..4
Putting 4 in 3, we get:
Putting 6 in 1, we get:
So, acceleration is given by:
Rate this question :
A ball falls on the ground from a height of 2.0 m and rebounds up to a height of 1.5 m. Find the coefficient of restitution.HC Verma - Concepts of Physics Part 1
A graph of x versus t is shown in Fig. 3.3. Choose correct alternatives from below.Physics - Exemplar
A particle executes the motion described by X(t) =X0(l - e-yt) t ≥ 0,
(a) Where does the particle start and with what velocity?
(b) Find maximum and minimum values of x (t), v (t), a (t). Show that x (t) and a (t) increase with time and v (t) decreases with time
Physics - Exemplar
A ball is dropped and its displacement vs time graph is as shown Fig. 3.4 (displacement x is from ground and all quantities are +ve upwards). (a) Plot qualitatively velocity vs time graph. (b) Plot qualitatively acceleration vs time graph.
Physics - Exemplar
A ball is bouncing elastically with a speed 1 m/s between walls of a railway compartment of size 10 m in a direction perpendicular to walls. The train is moving at a constant velocity of 10 m/s parallel to the direction of motion of the ball. As seen from the ground,Physics - Exemplar
A bird is tossing (flying to and fro) between two cars moving towards each other on a straight road. One car has a speed of 18 m/h while the other has the speed of 27km/h. The bird starts moving from first car towards the other and is moving with the speed of 36km/h and when the two cars were separated by 36 km. What is the total distance covered by the bird? What is the total displacement of the bird?Physics - Exemplar
A lift is coming from 8th floor and is just about to reach 4th floor. Taking ground floor as origin and positive direction upwards for all quantities, which one of the following is correct?Physics - Exemplar