When an object is moving with a constant velocity 10 m/s, (1) Find its accelerat

Question

When an object is moving with a constant velocity 10 m/s, (1) Find its acceleration at 20 sec. (2) Find its final velocity in 5 m. (3) Find its position at 10 sec. An object at rest is falling from 30 m above, (1) Find its acceleration at 2 sec. (2) Find its final velocity. (3) Find its velocity when it falls 5 m from initial position. (4) Find Its time when it has fallen 10 m from initial position. (5) Find its position when the velocity becomes 15 m/s. An object's initial position is 5m and initial velocity is 2 m/s. It accelerates with a = 2 m/s^2. (1) Find its velocity at 3 sec. (2) Find Its velocity at 7 m from Initial position. (3) Find Its position at 2 sec. (4) Find its position when the velocity becomes 100 m/s.

Explanation / Answer

1. Object is moving with a constant velocity.

(1) So, the acceleration will be zero irrespective of time unless the object chages its state of constant velocity motion.

(2) Final velocity at 5m will be 10 m/s as the object is in constant velocity motion.

(3) If we assume that the object started moving with 10 m/s

     Then, at t = 10 sec, S = vt = 10 x 10 = 100m

2. Object at rest is falling from 30 m above

(1) SInce the object is falling that means it is under the influence of gravitational acceleration.

     So, At t = 2 sec, a = 9.81 m/s2

(2) Final velocity means the velocity at which it collides with ground that is velocity acheived after   covering 30 m.

     From third equation of motion,    v2 = u2+2as

     Putting u = 0 m/s (started from rest), a = 9.81 m/s2 and    s = 30 m

     v2 = 02 + 2 x 9.81 x 30 = 588.6      or v = (588.6)1/2 = 24.26 m/s

(3) When it has fallen 5 m from initial position,

    v2 = u2 + 2as = 02 + 2 x 9.81 x 5 = 98.1   or v = (98.1)1/2 = 9.90 m/s

(4) When it has fallen 10 m from initial position,

     From second equation of motion

                    s = ut + 0.5 at2

      10 = 0 x t + 0.5 x 9.81 x t2

                                 t2 = 10/(0.5 x 9.81) = 2.0387    or t = (2.0387)1/2 = 1.4278 sec

(5) When the velocity becomes 15 m/s that is v = 15 m/s

                                 v2 = u2+2as

                                152 = 02 + 2 x 9.81 x s

                                 s = 225/(2 x 9.81) = 11.467 m   (from initial position)

3. Initial position of object, s = 5 m : Initial Velocity, u = 2 m/s : Acceleration a = 2 m/s2

      (1) From first equation of motion, v = u + at

          At, t = 3 sec   v = 2 + 2 x 3 = 8 m/s

      (2) Velocity at 7 m from initial position = v

                              v2 = u2+2as

                             v2 = 22 + 2 x 2 x 7 = 32     or v = (32)1/2 = 5.656 m/s

      (3) At t = 2 sec,

           s = ut + 0.5 at2

                       s = 2 x 2 + 0.5 x 2 x 22 = 8 m

      (4) When velocity   v = 100m/s

                v2 = u2+2as

                          1002 = 22 + 2 x 2 x s

                          s = (10000 - 4)/4 = 2499 m

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