Question

please bro solve this ​

Answer 1

Solution

It is a problem based on Kinematics.

Let us assume time elapsed for acceleration is t₁ and time elapsed for retardation is t₂ . Hence total time t = t₁ + t₂.

Case 1: Acceleration-

Given,

• u = 0
• a = α
• t = t₁

Applying first equation of motion we get:

→ v = 0 + αt₁

→ v = αt₁

This is the final velocity before the car starts to decelerate. Hence initial velocity of the car when it starts to decelerate would be αt₁.

Now Applying Second equation of motion, we can get the length traveled by the car. Applying the equation we get:

→ s₁ = (0)t₁ + 0.5( αt₁²)

→ s₁ = 0.5 ( αt₁² )   ... Eqn (1)

Case 2: Retardation-

Given,

• u =  αt₁
• a = β
• t = t₂

Therefore length traveled in t₂ second is given by the second equation of motion.

→ s₂ = (αt₁)t₂ + 0.5βt₂²   ... Eqn (2)

Now we know that, Average Speed is given as:

→ Total Distance Traveled / Total Time Taken

Substituting the values we get:

→ ( s₁ + s₂ ) / ( t₁ + t₂ )

→ [ 0.5 ( αt₁² ) + (αt₁)t₂ + 0.5βt₂² ] / t

→ [ 0.5 ( αt₁² + βt₂² ) + αt₁t₂ ] / t

This can be simplified and written as:

→ [ ( αt₁² + βt₂² ) + αt₁t₂ ] / 2t    [0.5 written as 1/2]

This is the required answer.