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 / s2

When that particle free falls towards the earth, there bounds to be some velocity. That velocity is depicted by v0. Velocity in that initial level is zero.

Therefore, v0 = 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 / s2

Solved examples

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:

1. Retardation
2. Distance traveled by car after the application of brakes

Solution

Let initial velocity be V0

Final velocity be V

Time when break is applied be t

As per the equation,

V = V0– 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 = V0– at

0 = 50 – 5a

a =

= 10 m /s2

This is the value of retardation.

In case of the travelled distance,

S = S0 +v0 t –at2

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 V0

Let final velocity be V

Time = t

According to formula, V = V0+ at

a =

=

=

= 1.5 m /s2

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