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When a particle moves with constant acceleration

  • The acceleration is said to be constant when both magnitude and direction of acceleration remain constant.
  • There will be one-dimensional motion if initial velocity and acceleration are parallel or anti-parallel to each other.

Some Important Notes

  • If a body starts from rest and moves with uniform acceleration then distance covered by the body in tsecond is proportional to t2 (i.e., s ∝ t2).
     
    So we can say that the ratio of distance covered in 1 s, 2 s, and 3 s is 12 : 22 : 32 or 1 : 4 : 9.
  • If a body starts from rest and moves with uniform acceleration, then the distance covered by the body in nth seconds is proportional to (2n – 1), i.e., sn ∝ (2n –1).
     
    So, we can say that the ratio of distance covered in 1st, 2nd, and 3rd, is 1 : 3 : 5.
  • A body moving with 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.
  • 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
     
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