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Question

A car accelerates from rest at a constant rate of 2 ms2 for some time. Then it retards at a constant rate of 4 ms2 and come to rest. It remains in motion for 6 s.

A
Its maximum speed is 8 ms1
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B
It maximum speed is 6 ms1
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C
It travelled a total distance of 24 m
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D
It travelled a total distance of 18 m
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Solution

The correct options are
A Its maximum speed is 8 ms1
C It travelled a total distance of 24 m
a1=2 ms2,a2=4ms2
v0=a1t1=2t1,v0=a2t2=4t2
t1+t2=6v02+v04=6
v0=8 ms

Distance during constant accelerated motion can be calculated as Vavgt. So,
AC=Vavgt1=v0+02t1
CB=Vavgt1=v0+02t2

Total distance travelled
S=AC+CB=12v0t1+12×v0t2
S=12v0[t1+t2]=12×8×6=24 m

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