Question

A ball rolling down a hill for 9 seconds accelerates from 3 m/s to 34.5 m/s. Its acceleration is m/s2.

Answer 1

Answer:

• Acceleration of ball = 3.5 m/s²

Explanation:

Given:

• Initial velocity of ball, u = 3 m/s
• Final velocity of ball, v = 34.5 m/s
• time taken for changing velocity, t = 9 s

To find:

• Acceleration of ball, a =?

Formula required:

• First equation of motion

       v = u + a t

[ where v is final velocity, u is initial velocity, t is time taken and a is acceleration ]

Solution:

Using first equation of motion

→ v = u + a t

( putting values )

→ 34.5 = 3 + a × 9

→ 34.5 - 3 = 9 a

→ 31.5 = 9 a

→ a = 31.5 / 9

→ a = 3.5 m/s²

Therefore,

• Acceleration of ball is 3.5 m/s².

Answer 2

Answer :-

✳Acceleration of the ball

= 3.5 m/s²

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★ Concept :-

Here the concept of Newton's Equations of motions is used. Newton developed these equations using his Laws of Motions which show relationship among distance, displacement,acceleration, velocity and time.

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★ Solution :-

Given,

▶Initial Velocity of the ball, u = 3 m/s

▶ Final Velocity of the ball, v = 34.5 m/s

▶ Time taken by the ball for journey, t = 9 sec

▶ Let the acceleration of the ball be 'a'.

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Here we can get our answer simply and easily by using the Newton's First Law of Motion.

This is formulated as :-

• v - u = at

where,

v is the final velocity of the ball,

u is the initial velocity of the ball,

a is the acceleration of the ball, and

t is the time taken by the ball for journey.

By applying the values in the equation, we get

✏ v - u = at

✏ 34.5 - 3 = a × 9

✏ 31.5 = a × 9

✏ a = 31.5 / 9 = 3.5

✏ a = 3.5 m/s²

Hence the acceleration of the ball = 3.5 m/s²

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★ More to know :-

• Acceleration is defined as rate of change of velocity of a body. It is given by, (v - u) / t ,where we get its dimensional formula as [L¹ / T²].

• Velocity is defined as rate of change of displacement of body. Its a vector quantity.

• Newton's Second equation of Motion :-

s = ut + ½(at²)

where, s is the displacement, u is the initial velocity, t is the time taken and a is the acceleration .

• Newton's Third Law of Motion :-

v² - u² = 2as

where, v is the final velocity, u is the initial velocity, a is the acceleration and s is the displacement.