Q.

Each of the four particles move along an x-axis. Their coordinates (in metres) as function of time (in seconds) are given by Particle 1: x(t)=3.5−2.7t3 Particle 2:x(t)=3.5+2.7t3 Particle 3: x(t)=3.5+2.7t2 Particle 4: x(t)=3.5−3.4t−2.7t2which of these particles is speeding up for t > 0?

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a

All four

b

only 1

c

only 1, 2 and 3

d

only 2, 3 and 4

answer is A.

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Detailed Solution

At A=0dxdt=0 for particles 1,2 and 3 and d2xdt2>0 for t>0 and dxdt=−3.4m/s for particle 4 and d2xdt2 is negative for t>0 Therefore for t>0;dxdt is increasing in all.
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