Question

For a body starting from rest, the displacement in 10 seconds, when it acquires 4m/s in 10s is

Answer 1

Given :-

Initial velocity of the body = 0 m/s

Velocity after 10 sec = 4 m/s

To Find :-

The displacement covered by the body.

Analysis :-

Firstly substitute the given values in the question using the first equation of motion and find the acceleration accordingly.

Then using the second equation of motion substitute the values we got and find the displacement accordingly.

Solution :-

Using the formula,

$\underline{\boxed{\sf First \ equation \ of \ motion=v=u+at}}$

We know that,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time taken

Given that,

Final velocity (v) = 4 m/s

Initial velocity (u) = 0 m/s

Time taken (t) = 10 sec

Substituting their values,

⇒ a = (v-u) / t

⇒ a = (4 - 0) / 10

⇒ a = 4/10

⇒ a = 0.4 m/s²

Using the formula,

$\underline{\boxed{\sf Second \ equation \ of \ motion=s=ut+\dfrac{1}{2} at^2}}$

We know that,

• s = Displacement
• u = Initial velocity
• t = Time taken
• a = Acceleration

Given that,

Initial velocity (u) = 0 m/s

Time taken (t) = 10 sec

Acceleration (a) = 0.4 m/s²

Substituting their values,

⇒ s = 0 × 10 + (1/2) × 0.4 × 10²

⇒ s = (1/2) × 0.4 × 10²

⇒ s = (0.4 × 100) / 2

⇒ s = 40/2

⇒ s = 20 m

Therefore, the displacement is 20 m.