When it is about acceleration caused due to gravity, particles usually move in 2 directions. It is either in upward side or towards down.

**Calculation of particles which moves in vertically downward direction**

A particle experiencing free fall under gravity, or in layman term, when the earth attracts it, in that situation, that particle will be directly accelerated towards earth’s center.

While calculating the equation for acceleration, ‘a’ is replaced by ‘g’ (gravity). As per that, the new equation stands at,

a = + g

+ g = 9.81 m / s^{2}

When that particle free falls towards the earth, there bounds to be some velocity. That velocity is depicted by v_{0}. Velocity in that initial level is zero.

Therefore, v_{0} = 0.

**Calculation of particles which moves in vertically downward direction**

As per the equation, in this case, acceleration of a particle, which is ‘a’ is replaced by ‘-g’.after the replacement, the new equation stands to be,

a = – g

– g = – 9.81 m / s^{2}

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**Solved examples**

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**Example 1**

Velocity of a moving car is found to be 50 m / s. Suddenly in 5 seconds break is applied and the car is brought to rest. From this information find out:

- Retardation
- Distance traveled by car after the application of brakes

**Solution**

Let initial velocity be V_{0}

Final velocity be V

Time when break is applied be t

As per the equation,

V = V_{0}– at

We know value of initial velocity and time, but not of final velocity. So, we will consider the final velocity to be 0.

V = V_{0}– at

0 = 50 – 5a

a =

= 10 m /s^{2}

This is the value of retardation.

In case of the travelled distance,

S = S_{0} +v_{0} t –at^{2}

S = 0 + 50 x 5 -x 6 x(5)^{2}

= 250 – 75

= 175m

**Example 2**

A moving body’s velocity is found to be 4 m / s. After an interval of 4 seconds; it was found that the new velocity is 10 m / s. Calculate the uniform acceleration of that body.

**Solution**

Here, let initial velocity be V_{0}

Let final velocity be V

Time = t

According to formula, V = V_{0}+ at

a =

=

=

= 1.5 m /s^{2}

**Links of Previous Main Topic:-**

- Introduction about distributed forces
- Area moments of inertia in rectangular and polar coordinates
- Mass moment of inertia introduction
- Work done by force
- Kinematics of particles
- Plane motion

**Links of Next Mechanical Engineering Topics:-**