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Question

A car, starting from rest, has a constant acceleration a1 for a time interval t1 during which it covers a distance s1 . In the next time interval t2, the car has a constant retardation a2 and comes to rest after covering a distance s2 in time t2. Which of the following is correct?


A

a1a2=s1s2=t1t2

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B

a1a2=s2s1=t1t2

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C

a1a2=s2s1=t2t2

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D

a1a2=s2s1=t2t1

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Solution

The correct option is D

a1a2=s2s1=t2t1


Step 1: Given data

A car, starting from rest, has a constant acceleration a1 for a time interval t1 during which it covers a distance s1 .

In the next time interval t2, the car has constant retardation a2 and comes to rest after covering a distance s2 in time t2.

Step 2: Consider case 1

A car, starting from rest, has a constant acceleration a1 for a time interval t1 during which it covers s1 distance. So,

Initial velocity, u=0

The second equation of motion is,

s=ut+12at2

Here, s is the distance travelled time t, u is the initial velocity, and a is the acceleration of the body in motion.

s1=12a1t12 ------- 1

And velocity after time t1,v1=a1t1

Step 3: Consider case 2

In the next interval t2, the car has constant retardation a2 and comes to rest after covering a distance s2 in time interval t₂.

So,

Velocity after time t2,v2=u2-a2t2

Here,

u2=v1

=a1t1

v2=a1t1-a2t2

But the body comes to rest so v2=0

So,

a1t1-a2t2=0

a1a2=t2t1 --------- 2

Now, the distance covered in t2 time is,

s2=12a2t22 ------------ 3

From equations 1 and 3, we get,

s1s2=a1t12a2t22

From the equation 2 we get,

s1s2=t1t2 ------------ 4

From equations 2 and 4 we get,

a1a2=s2s1=t2t1

Hence, option D is the correct answer.


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