Question

8. An object starts from rest at the origin and moves along the x-axis with a constant acceleration of 4 ms². Its average velocity as it goes from x=2m to x= 8 m is:​

Answer 1

Step-by-step explanation:

acceleration of the object, a = 4 m/s²

distance covered, d₁ = 2m and d₂ = 8m

To Find: average velocity, V.

Solution:

To calculate V, the formula used:

v² - u² = 2 as ⇒ Third Law of Motion Equation

here, v is the final velocity

u is the initial velocity, i.e. u =0 m/s

a is the acceleration

s is the distance covered

Average velocity, V = (velocity at d₁ + velocity at d₂) / 2

V = (v₁ + v₂)/ 2 ⇒ 1

Applying the 3rd law of motion equation formula:

For v₁ :

v₁ ² - u² = 2 x a x d₁

v₁ ² - 0² = 2 x 4 x 2

v₁ ² = 4 x 4

= 16

v₁ = √16

= 4

v₁ = 4 m/s

For v₁ :

v₂² - u² = 2 x a x d₂

v₂ ² - 0² = 2 x 4 x 8

v₂ ² = 8 x 8

= 64

v₂ = √64

= 8

v₂ = 8 m/s

Putting the value of v₁ and v₂ in equation 1:

V = 4 + 8 / 2

= 12 / 2

= 6

V = 6 m/s

Hence, the average speed of the object is 6 m/s.