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Question

Two cars start off to race with velocities 4 m/s and 2 m/s and travel in a straight line with uniform accelerations 1 m/s2 and 2 m/s2 respectively. If they reach the final point at the same time instant, then what is the length of the path?

A
12 m
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B
18 m
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C
24 m
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D
30 m
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Solution

The correct option is C 24 m
Let the two cars be car A and car B.
For car A:
s1=ut+12at2s1=4t+12×1×t2 (using second eqn of motion)
For car B:
s2=ut+12at2s1=2t+12×2×t2 (using second eqn of motion)
On equating the distance, s1=s2
4t+12×1×t2=2t+12×2×t2
2t=t22
t=4 s
Putting the value in any one of the equations, we get
s=4×4+12×1×42=24 m

Alternate sol:
Initial velocity of 1 w.r.t 2, u12=42=2 m/s
Acceleration of 1 w.r.t 2, a12=12=1 m/s2
Finally, displacement of 1 w.r.t 2, S12=0
Using second equation of motion,
S12=u12+12a12t2
0=2t12×1×t2t=4 s
Distance travelled by 1st body =ut+12at2
=4×4+12×1×42=24 m

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