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Questions  

A car is moving with uniform acceleration along a straight line between two stops X and Y. Its speed at X and Y are 2 ms-1 and 14 ms-1, Then

a
its speed at mid-point of XY is 10 ms-1
b
its speed at a point A such that XA:AY=1:3 is 5 ms-1
c
the time to go from X to the mid-point of XY is double of that to go from mid-point to Y
d
the distance travelled in first half of the total time is half of the distance travelled in the second half of the time

detailed solution

Correct option is A

(14)2=(2)2+2as∴2as=192 unitsAt mid point, v2=(2)2+2as2=4+1922=100∴ v=10 m/sXA:AY=1:3XA=14s and AY=34sv12=(2)2+2as4=4+1924=52v1=52≠5 m/s10=2+at1(v=u+at)∴t1=8a14=10+at2∴t2=4a or t1=2t2S1=(2t)+12at2= distance travelled in first halfS2=2(2t)+12a(2t)2S3=S2-S1= distance travelled in second half. We can see that,S1≠S32

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