Question

Amber was driving a car with speed 72 km / hr. He observes a dog at 10 meter ahead of him. Find the minimum retardation applied if he has to save the dog.
1. 20  m / s ²
2. 25 m / s 2
3. 40 m / s 2
4. 30 m / s 2

Answer 1

Correct Answer - Option 1 : 20  m / s ²

Concept:

Retardation:

• It is the process of reduction of speed. 
• It is the negative of acceleration. 

Acceleration:

• It is the rate of change of velocity with respect to time.
• It is a vector quantity. 

Equation of Motion

For a uniformly accelerated motion, the equations of motion is represented as 

v = u + at -- (1)

\(S = ut + \frac{1}{2}at^2\) -- (2)

v 2 = u 2 + 2as -- (3)

Where v is final velocity, u is initial velocity, t is the time interval for which the force is applied, s is displacement

Calculation:

Given, initial speed of Amber u = 72 km / hr 

In m / s

\(72 \times \frac{5}{18} m/s = 20\ m/s\)

u = 20 m /s

The final speed should be zero, as he has to stop the car

v = 0 

distance travelled s = 10 m

as car is 10 m ahead

Now applying this in third equation

(0) ² = (20) ² +  2 a (10 )

⇒ 0 = 400 + 20 a

⇒ a = - 20

So, acceleration is - 20 m / s²

So, deacceleration is d = - a = - (- 20 m / s² ) = 20 m / s²

So, the correct option is 20 m / s 2