Question

A bus moving with a velocity of 60 m/s comes to stop after applying brakes. If it takes 3 seconds to stop then calculate the acceleration it produces.

Answer 1

Given :

• Initial Velocity (u) = 60 m/s

• Final Velocity (v) = 0 m/s

• Time (t) = 3 seconds

To Find :

• Acceleration produced (a)

Solution :

We know that, acceleration is measure of the change in velocity of an object per unit time.

★ Acceleration = Final Velocity - Initial Velocity/Time taken

→ a = $\sf\dfrac{0-60}{3}$

→ a = $\sf\cancel\dfrac{-60}{3}$

→ a = - 20 m/s²

$\therefore$ Acceleration produced is - 20 m/s².

The negative sign of acceleration means that it is retardation. So, we can also say that the bus has a retardation of + 20m/s.

Answer 2

Given :-

◉ Initial velocity of bus, u = 60 m/s

◉ Final velocity of bus, v = 0 m/s [∵ The bus comes to rest]

◉ Time taken by the bus to come to rest, t = 3s

To Find :-

◉ Acceleration produced by the bus after applying the brakes.

Solution :-

We need to find the acceleration, So

By the first equation of motion,

⇒ v = u + at

Substituting values,

⇒ 0 = 60 + a×3

⇒ -60 = 3a

⇒ a = -20 m/s²

Hence, The acceleration produced was -20 m/s²

Some Information :-

◉ The negative acceleration is also known as Deceleration or Retardation.

◉ Other equations of motion:

• h = ut + (at²)/2
• 2as = v² - u²

Where,

• h = Height reached
• u = Initial Velocity
• v = Final Velocity
• t = Time taken
• a = Acceleration

◉ Acceleration is the rate of change of velocity per unit time, It is a vector quantity, Meaning It has both magnitude and direction.