Question

Two cars A and B start of to race on straight path with initial velocities of 8 metre per second 5 metre per second square respectively car A moves with uniform acceleration 1 metre per second square and car B moves with uniform acceleration of 1.1 M per second square if both the cars reach the winning post together. then
A) time taken to reach winning post is 60 seconds
B) length of track is 2280 metres.
C) car B was ahead of car A 10 seconds before finish.
D) car A was ahead of car B 10 seconds before finish.

Answer 1

For car A :

u = 8 m/s

a = 1 m/s^2

let's suppose it takes t time to reach the winning post

so, s = u t + 1/2 a t^2

or, s = 8 t + 1/2 × 1 × t^2

or, s = 8 t + 0.5 t^2 ______________1

For car B :

u = 5 m/s

a = 1.1 m/s^2

so, s = u t + 1/2 a t^2

or, s = 5 t + 1/2 × 1.1 × t^2

or, s = 5 t + 0.55 t^2 ____________2

As both the car reached the destination together so time and s will be the same for both

so, eqn 1 = eqn 2

or, 5 t + 0.55 t^2 = 8 t + 0.5 t^2

or, 8 t - 5 t = 0.55 t^2 - 0.5 t^2

or, 3 t = 0.05 t^2

or, 0.05 t^2 - 3 t = 0

or, t ( 0.05 t - 3) = 0

or, t = 0 or t = 3/0.05 = 300/5 = 60 s

so, they will reach destination after 60 s

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putting value of t = 60 s in any one , let's say eqn 1

we get ,

s = 8 × 60 + 0.5 × 60^2

s = 480 + 1800 = 2280 m

So, length of track is 2280 m.

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At t = 60 - 10 = 50 s { 10 s ahead of finish }

A : s = 8×50+0.5×50^2 = 400 + 1250 = 1650m

B : s = 5×50+0.55×50^2 = 250 + 1375 = 1625m

So, Car A was ahead of car B by 25 m 10 s before finish .

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Hence A , B and D are correct options.