Formulas and Important Points

1. v = u+ at     ...    s=ut+(1/2)t²      .....     v²-u_² = 2as  .....

               ........

2. If a body starts from rest and moves with uniform acceleration then distance covered by the body in t sec is proportional to t² so the  ratio of distance covered in 1 sec, 2 sec and  3 sec is  1 : 4 : 9.

3.If a body starts from rest and moves with uniform acceleration then distance covered by the body in nth sec is proportional to (2n-1) so the ratio of distance covered in 1st sec, 2nd sec and 3rd sec is 1 : 3 : 5.....

4.If an object is accelerated with an acceleration a₁ for a time t₁ and with an acceleration a₂for a time t₂, then average acceleration for entire time is given by

a_av = ((a₁t₁ + a₂t₂) / (t₁ + t₂))

5.If an object starting from rest accelerates at a constant rate α for certain time and then retards at a constant rate β and finally comes to rest after total time t from the start, then maximum speed acquired by the object,

v_max = (α β t)/(α + β) and total distance covered by the object in this time, s = (α β t²)/(2 (α + β))

6.  A body moving with a velocity u is stopped by application of brakes after covering a distance s. If the same body moves with velocity nu and same braking force is applied on it then it will come to rest after covering a distance of n²s.

7.A particle moving with uniform acceleration from A to B along a straight line has velocities v₁ and v₂ at A and B respectively. If C is the mid-point between A and B then velocity of the particle at C is equal to

8.Motion of an object can be represented by a positive – time (x – t) graph. For an object at rest, x – t graph is a straight line parallel to the time axis. For uniform linear motion, x – t graph is a straight line with a constant slope. The slope of line represents uniform speed of the object.

9.If straight line x – t graphs for two objects subtend angles θ­₁ and θ­₂ respectively from the time axis, then magnitudes of velocities of these objects v₁ and v₂ are corrected as:     (v₁/v₂) = (tan θ­₁) / (tan θ­₂)

10. For uniformly accelerated motion, x – t graph is a parabola. If x – t curve is bending towards position axis, then acceleration is positive. On the other hand, if x – t curve is bending towards time axis, then acceleration is negative for the object.

11. For uniform linear motion, velocity-time (v – t) graph is a straight line parallel to the time axis. However, for uniformly accelerated motion, v – t graph is a straight line with a constant slope. The constant slope of v – t graph gives the value of uniform acceleration.

12.  Area covered between the v – t graph and time axis gives the magnitude of displacement and distance travelled by the object for a given time interval.Total area, considering its sign, between v – t graph and time axis gives the displacement. However, total area, considering without sign, gives the distance travelled during the given time interval.

13. For uniformly accelerated motion, the acceleration-time (a – t) graph is a straight line parallel to time axis. The area covered between the a – t graph and time axis gives the value of change in speed (or magnitude of change in velocity) of the moving object.

14. Direction of motion of an object is governed by its velocity and not by its acceleration. Moreover, acceleration of an object may be nonzero at an instant when its velocity is zero or vice versa.

15. When an object is released near the surface of the Earth, it is accelerated downwards due to the force of gravity. Linear motion of an object under the action of force of gravity alone is called free fall, in which acceleration of the object a = g = 9.8 m s^-2 in vertically downward direction.

16.  For linear motion along vertical direction generally upward direction is taken to be positive upward direction is taken to be positive and the downward direction negative.

17.If an object is just dropped (u – 0) from a height h and falls through a vertical distance y in time t and acquires a velocity v, then

v = -gt, -y = (-1/2) gt²

and v² = 2gy

Moreover, the object will reach the ground after a time,    and will strike the ground with a final velocity v = -(2gh)^1/2.

18.If an object is projected upwards from the ground with an initial velocity u, then neglecting air friction, we have

Maximum height attained by the object,h = u²/2g 

Time to reach the highest point,

t = u/g

and total time of flight,

t = 2u/g

When the object falls back on the ground, its speed is again u but final velocity is –u (on account of change in direction of motion).

19. Let an object be dropped from a height h and it reaches the ground after time t. if two objects are projected from same height, one with a velocity u upwards and the other with velocity u downwards and these objects take times t₁ and t₂ respectively to reach the ground, then (t₁t₂)^1/2 = t.