Question

A man starting from rest attains velocity of 30m/s after covering discplacement of 100m.Calculate acceleration and time taken?​

Answer 1

Given :

Initial velocity of the man = zero.

Final velocity of the man = 30m/s.

Displacement = 100m.

To find :

The acceleration and time taken by the man.

Solution :

Acceleration is defined as the rate of change of velocity.

• It is a vector quantity having both magnitude as well as direction.
• It can be positive, negative or zero.
• SI unit of accerlation is metre per second square (m/s²).
• Dimension formula : [M¹L¹T‾¹]

As we are provided with initial velocity, final velocity and displacement we can use 3rd equation of kenimatics that is,

v² - u² = 2as

Where,

• v denotes final velocity
• u denotes initial velocity
• a denotes acceleration
• s denotes displacement

substituting all the given values in the equation,

v² - u² = 2as

(30)² - (0)² = 2(a)(100)

900 = 200a

a = 900/200

a = 4.5 m/s².

thus, the acceleration of the man is 4.5m/s².

Now, to find time taken we can use first equation of kenimatics that is,

v = u + at

substituting all the values,

30 = 0 + (4.5)t

30 = 4.5t

t = 30/4.5

t = 6.667 sec.$⠀$

thus, time taken by the man is 6.667 sec.