Question

A point moves along X-axis initially at rest. Its acceleration is a = (6t + 5) m/s². The distance covered in 2s, if it starts from the origin is given by ______.

विकल्प

• 6 m

• 12 m

• 16 m

• 18 m

Answer 1

A point moves along X-axis initially at rest. Its acceleration is a = (6t + 5) m/s². The distance covered in 2s, if it starts from the origin is given by 18 m.

Explanation:

Given, acceleration, a = (6t + 5) m/s²

`a = (dv)/(dt)` = 6t + 5

⇒ dv = (6t + 5) dt

⇒ ∫ dv = ∫ (6t + 5)dt

⇒ v = 3t² + 5t + c

where c is the constant of integration.

When t = 0, v = 0, so c = 0

Therefore, v = 3t² + 5t

⇒ ds = (3t² + 5t) dt `[∵ v = (ds)/(dt)]`

From 0 to 2s, we have

`int_0^sds = int_0^2(3t^2 + 5t)dt`

s = `(t^3 + 5/2t^2)_0^2  = 8 + 10 = 18` m