When displacement is proportional to the cube of time?

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An object, moving with a speed of 6.25 ms-1, is decelerated at a rate given bydvdt=-2.5v, where v is the instantaneous speed. The time taken by the object, to come to rest, would be:

A projectile is fired from the surface of the earth with a velocity of 5 ms-1 and angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3 ms-1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in ms-2)

1. Definitions:

(i) Total length of path covered by the particle in a time interval is called distance. Displacement vector or displacement is the minimum distance and directed from the initial position to final position.

(ii) Distance is greater than or equal to magnitude of displacement.

(iii) Speed is the rate of distance covered, v=dsdt.

(iv) Velocity is the rate of displacement covered, v→=ds→dt.

(v) Average velocity is the ratio of total displacement to the total time.

(vi) Average speed is the ratio of total distance to the total time.

2. Graphical representation of motion:

(i) Slope of distance-time graph gives speed and that of the displacement-time graph gives velocity.

(ii) Slope of velocity-time graph gives acceleration.

(iii) Area of velocity-time graph gives displacement.

(iv) Area of speed-time graph gives distance.

3. Equations of motion for constant acceleration:

(i) v=u+at

(ii) s=ut+12at2

(iii) v2-u2=2as.

(iv) s=v+u2t

4. Relative motion:

(i) If SA→ and SB→ are the displacements of A and B, the displacement of A with respect to B becomes  SA→-SB→.

(ii) If VA→ and VB→ are the velocities of A and B, the velocity of A with respect to B becomes VA→-VB→.

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NEET 2023 - Target Batch - Aryan Raj Singh

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NEET 2023 - Target Batch - Aryan Raj Singh

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