Question

a car started from rest and accelerated with uniform acceleration a1 for 10secs then decelerated with uniform deceleration A2 to finally come to rest in next 5secs. show that a1/A2=1/2​

Answer 1

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Answer 2

Given :

During acceleration phase :

final velocity = $v_1$

initial velocity =$u$

acceleration $= a_1$

During deceleration phase :

final velocity = $v_2$ = 0

initial velocity = $v_1$

acceleration $= A_2$

To prove :

$\frac{a_1}{A_2} = \frac{1}{2}$

Explanation:

Case 1 : During acceleration phase , we will substitute the values given in the following equation;

$v= u + at$

$t_1 = 10 sec$

$v_1 = 0+ 10a_1$

$v_1 = 10a_1$

Case 2 : During deceleration phase , final velocity from case 1 becomes initial velocity of case 2.

Therefore , substituting again in the same equation of motion, we have ;

$t = 5sec$

$v_2 = v_1 - 5 A_2$ ( negative sign is due to deceleration )

substituting $v_2 = 0$ and $v_1 = 10a_1$ from first equation, we get;

$0 = u +10a_1 - 5A_2$

Also $u = 0$ , we have ,

$5 \times\ A_2 = 10 \times a_1$

$\frac{a_1}{A_2} = \frac{5}{10}= \frac{1}{2}$

Hence proved , $\frac{a_1}{A_2} = \frac{1}{2}$