Question

A body of mass 8.0 kg is initially at rest on a horizontal frictionless surface. A force of 18 N acts on it and accelerates it to a final velocity of 12 m/s. Calculate (a) the distance travelled, (b) the work done by the force, (c) the final KE of the body,

Answer 1

Hi.

Here is the answer---

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Mass = 8 kg.
Force = 18 N.

Using Newton Second Law of Motion,

  F = Mass × Acceleration
   18  = 8 × Acceleration
Acceleration = 18/8
                     = 9/4
                     = 2.25 m/s²

Now, Initial Velocity(u)  = 0
Final Velocity(v) = 12 m/s.

Thus,
    $Acceleration = \frac{v - u}{t}$
              2.25 = (12 - 0)/t
                    t = 12/2.25 seconds.

(a)

Using the Formula,

   Speed = Distance/Time
   12 = Distance/(12/2.25)
Distance = 12 × 12/2.25
               = 64 m.

(b)

Work Done = Force × Distance
                   = 18 × 64
                   = 1152 J.

(c) Kinetic Energy = (1/2)mv²
                             = (1/2) × 8 × (12)²
                             = 576 J.


Hope it helps.