Question

A cricket ball of mass 150 kg moving at aspeed of 25m/s is brought to rest by a player in 0.03 s . Find the average force applied by the player.​

Answer 1

Given :-

Mass of the cricket ball = 150 kg

Initial velocity of the ball = 25 m/s

Time taken for the change in velocity = 0.03 sec

To Find :-

The average force applied by the player.

Analysis :-

Here we are given with the time taken, mass, initial velocity and the final velocity of the body.

Using the first equation of motion, you can easily substitute the given values and find the acceleration accordingly.

Then substitute the values you got such that force is equal to mass multiplied by acceleration and find the force.

Solution :-

We know that,

• u = Initial velocity
• a = Acceleration
• m = Mass
• v = Final velocity
• f = Force

Using the formula,

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

Given that,

Initial velocity (u) = 25 m/s

Final velocity (v) = 0 m/s

Time taken (t) = 0.03 sec

Substituting their values,

⇒ 0 = 25 + (a) 0.03

⇒ a = (v-u) / t

⇒ a = (0-25) / 0.03

⇒ a = -2500/3 m/s

Using the formula,

$\underline{\boxed{\sf Force=Mass \times Acceleration}}$

Given that,

Mass (m) = 150 kg

Acceleration (a) = -2500/3 m/s

Substituting their values,

⇒ f = ma

⇒ f = 150 × -2500/3

⇒ f = -375000/3

⇒ f = -125000 N

Therefore, the average force applied by the player is -125000 N.

Answer 2

Given :-

• Mass of the cricket ball = 150 kg

• Initial velocity of the ball = 25 m/s

• Time taken for the change in velocity = 0.03 sec

To Find :-

• The average force applied by the player.

Analysis :-

Here we are given with the time taken, mass, initial velocity and the final velocity of the body.

Using the first equation of motion, you can easily substitute the given values and find the acceleration accordingly.

Then substitute the values you got such that force is equal to mass multiplied by acceleration and find the force.

Solution :-

We know that,

• u = Initial velocity
• a = Acceleration
• m = Mass
• v = Final velocity
• f = Force

Using the formula,

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

Given that,

• Initial velocity (u) = 25 m/s

• Final velocity (v) = 0 m/s

• Time taken (t) = 0.03 sec

Substituting their values,

⇒ 0 = 25 + (a) 0.03

⇒ a = (v-u) / t

⇒ a = (0-25) / 0.03

⇒ a = -2500/3 m/s

Using the formula,

$\underline{\boxed{\sf Force=Mass \times Acceleration}}$

Given that,

• Mass (m) = 150 kg

• Acceleration (a) = -2500/3 m/s

Substituting their values,

⇒ f = ma

⇒ f = 150 × -2500/3

⇒ f = -375000/3

⇒ f = -125000 N

Therefore, the average force applied by the player is -125000 N.