Question

The velocity of an object is given by v=6t3i+t2j m/S.find it's acceleration at t=2s

Answer 1

Correct Question:

The velocity of an object is given by v = 6 t³ i + t² j m/s. Find it's acceleration at t=2 sec.

Answer:

• The acceleration (a) of the particle at t = 2 sec is 72 i + 4 j m/s²

Given:

1. Given Equation v = 6 t³ i + t² j m/s
2. Time period (t) = 2 sec

Explanation:

$\rule{300}{1.5}$

Firstly we need to find the acceleration of the object.

We Know,

⇒ a = d v / d t

Substituting the values,

⇒ a = d ( 6 t³ i + t² j ) / d t

Differentiating,

⇒ a = (3 × 6) t⁽³⁻¹⁾ i + (1 × 2) t⁽²⁻¹⁾ j

⇒ a = 18 × t⁽³⁻¹⁾ i + 2 t⁽²⁻¹⁾ j

⇒ a = 18 t² i + 2 t j

⇒ a = 18 t² i + 2 t j m/s²

∴ We Got the acceleration.

$\rule{300}{1.5}$

$\rule{300}{1.5}$

From above equation,

⇒ a = 18 t² i + 2 t j

Substituting the value of time,

⇒ a = 18 × (2)² i + 2 × (2) j

⇒ a = 18 × 4 i + 2 × 2 j

⇒ a = 72 i + 4 j

⇒ a = 72 i + 4 j m/s²

∴ The acceleration (a) of the particle at t = 2 sec is 72 i + 4 j m/s².

$\rule{300}{1.5}$

Answer 2

$</p><p>\tt{\purple{\huge{Question \: - }}}$

• The velocity of an object is given by v = 6 t³ i + t² j m/s. Find it's acceleration at t=2 sec.

$</p><p>\tt{\red{Answer \: - }}$

The Required Acceleration Is 72 i + 4 j m/s²

$</p><p>\tt{\orange{Step-By-Step-Explaination \: - }}$

• v = 6 t³ i + t² j m/s

• t = 2 sec.

$</p><p>\tt{\blue{ a = d v / d t}}$

Substituting -

$</p><p>\tt{\red{ a = d ( 6 t³ i + t² j ) / d t}}$

Differentiating,

$</p><p>\tt{\blue{ a = 18 t² i + 2 t j m/s²}}$

Substituting the value of time,

$</p><p>\tt{\purple{a = 72 i + 4 j m/s²}}$