Question

A motor car of mass 1200 kg is moving along a strainline with the uniform velocity of 90km/hr. its velocity is slowed down to 18km/hr in 4sec calculate the acceleration and change it momentum of magnitude of force​

Answer 1

Given :-

Mass of the motor car = 1200 kg

Initial velocity of the motor car = 90 km/h

Final velocity of the motor car = 18 km/h

Time taken by the motor car = 4 sec

To Find :-

The acceleration.

Change in momentum.

The magnitude of force.

Analysis :-

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

Firstly, using the first equation of motion find the acceleration of the motor car.

Then using the formula of change in momentum, substitute the values we got and find the change in momentum.

Then using the formula of force, you can easily find the magnitude of force!

Solution :-

We know that,

• u = Initial velocity
• t = Time
• a = Acceleration
• v = Final velocity

Using the formula,

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

Given that,

Initial velocity (u) = 90 km/h = 25 m/s

Final velocity (v) = 18 km/h = 5 m/s

Time (t) = 4 sec

Substituting their values,

⇒ 5 = 25 + a × 4

⇒ 5 = 25 + 4a

⇒ 4a = 5 - 25

⇒ 4a = -20

⇒ a = -20/4

⇒ a = -5 m/s²

Therefore, the acceleration is -5 m/s².

We know that,

• p = Momentum
• u = Initial velocity
• m = Mass
• v = Final velocity

Using the formula,

$\underline{\boxed{\sf Change \ in \ momentum= m(v-u) }}$

Given that,

Mass (m) = 1200 kg

Final velocity (v) = 5 m/s

Initial velocity (u) = 25 m/s

Substituting their values,

⇒ p = 1200 × (5 - 25)

⇒ p = 1200 × -20

⇒ p = -24000 kgm/s

Therefore, the change in momentum is -24000 kgm/s.

We know that,

• f = Force
• a = Acceleration
• m = Mass

Using the formula,

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

Given that,

Mass (m) = 1200 kg

Acceleration (a) = -5 m/s

Substituting their values,

⇒ f = ma

⇒ f = 1200 × -5

⇒ f = -6000 N

Therefore, the magnitude of force is -6000 N.

Answer 2

Given :

• Mass (m) = 1200 kg
• Initial velocity (u) = 90 km/hr = 25 m/s
• Final velocity (v) = 18 km/hr = 5 m/s
• Time taken (t) = 4 sec

To find :

• Acceleration (a)
• Change in momentum (p)
• Force (f)

Solution :

★ We know the first equation of motion:-

• v = u + at

→ 5 = 25 + (a × 4)

→ 5 = 25 + 4a

→ 5 - 25 = 4a

→ -20 = 4a

→ -20/4 = a

→ -5 = a

→ a = -5

★ We know the formula:-

• p = m(v - u)

→ p = 1200(5 - 25)

→ p = 1200 × (-20)

→ p = -24000 kgm/s

★ We know the formula:-

• Force = Mass × Acceleration

→ Force = 1200 × (-5)

→ Force = -6000 N

Answer :

• The acceleration = -5 m/s²
• Change in momentum = -24000 kgm/s
• Force = -6000 N