**1.8.1 Particle Moving Vertically Downward**

When a particle is free falling under the attraction of the earth, the particle will be

subjected to an acceleration directed towards the centre of the earth.

All equation involving ‘a’ will be replaced by a= + g (= 9.81 m/s^{2}). If it is a free fall,

the initial velocity is zero, i.e., v_{0} = 0. If there is some initial velocity, then the velocity = v0.

**1.8.2 Particle Moving Vertically Upwards**

In this case, we have to take, a= – g (-9.81 m/ s^{2}) in ail the governing equations involving

‘a’.

**SOLVED EXAMPLES**

**Example 1.1.** A body is moving with a velocity of 4 m/s. After 4 seconds the velocity of the body becomes 10 m/s. Determine the uniform acceleration of the body

**Solution. **v =v_{0} +at

** **10 =4+a x4

A = 10-4 /4 = 6/4 = 1.5 m /s^{2}.

**Example 1.2.** A motorcycle is moving with a velocity of 30 m/s. The motorcycle is brought to rest by applying brake in 5 seconds. Find (i) the retardation ; (ii) distance travelled by the motorcycle after applying brake

**Solution.** v_{0} =30 m/s

v = 0

t = 5 s

v = v_{0} –at

0 = 30 –a x5

a = 30 /5 = 6 m/s^{2} retardation.

We know S = S0 +v_{0} t – 1/2 at^{2}

S = 0 +30 x 5 -1/2 x 6 x(5)^{2}

= 150 – 75 = 75m.