Question

A 1000 kg vehicle moving with a speed of 20 metre per second is brought to rest in a distance of 50 metre.. find the acceleration... the actual force acted by the brakes may be slightly less than that calculated in number.. give reason

Answer 1

Solution:

Given:

=> Mass of the vehicle (m) = 1000 kg.

=> Initial Velocity (u) = 20 m/s

=> Final velocity (v) = 0 m/s

=> Distance travelled (s) = 50 m

To Find:

=> Acceleration (a).

Formula used:

=> v² = u² + 2as

=> F = ma

Now,

By using 3rd equation of motion we find acceleration,

=> v² = u² + 2as

=> 0 = (20)² + 100a

=> 0 - 400 = 100 a

=> -400 = 100 a

=> a = -400/100

=> a = -4 m/s²

This shows that the acceleration is in opposite direction that means it is retardation.

Now,

=> Force = mass × acceleration

=> Force = 1000 kg × (-4 m/s²)

=> Force = -4000 N.

Force is in negative means it is unbalance force.

Answer 2

Answer :

The unbalanced force is 4000 Newtons.

Step-by-step explanation:

Given :

Mass of vehicle = 1000 kg

Initial speed (u) = 20 m/s

Distance traveled (s) = 50 meters

Final speed (v) = 0 m/s

To Find :

The accelration.

Now,

★ Consider as -

The acceleration as - a.

We know that :

$\bigstar\;\boxed{\sf v^2 = u^2 + 2as}}$

Values in Equation,

$\implies \sf v^2 = u^2 + 2as$

[tex]\sf \implies 0^2 = 20^2 + 2 \times a \times 50 [/tex]

$\implies \sf a=-\dfrac{400}{100}$

$\implies \bf a=-4 m/s^2$

We also know that :

$\bigstar\;\boxed{\sf Force=Mass \times Acceleration.}}$

Values in Equation,

Force = - 1000 × 4

Force = - 4000 N

Here,

The force is in negative which implies that,

It is unbalance force.

∴ The unbalanced force is 4000 Newtons.

$\rule{300}{1.5}$

★ Points to Remember -

• Negative means that it is opposite to the direction of speed.
• Force is in negative means it is unbalance force.