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The position of a particle as a function of time is given by x(t)=ln(2t+3) for all positive t , where x is in meters and t is in seconds. What is the particle's acceleration at t=10sec ? A −231​m/s2 B −232​m/s2 C −5294​m/s2 D −234​m/s2 E −51​m/s2

The position of a particle as a function of time is given by x(t)=ln(2t+3) for all positive t, where x is in meters and t is in seconds.
What is the particle's acceleration at 
t=10sec?
A
−231​m/s2
B
−232​m/s2
C
−5294​m/s2
D
−234​m/s2
E
−51​m/s2

Grade:11

1 Answers

ankit singh
askIITians Faculty 614 Points
3 years ago

ANSWER

Position of the particle            x(t)=ln(2t+3)  m

Differentiating w.r.t time we get its velocity        v(t)=dtd[x(t)]=2t+32    m/s
 
Differentiating again w.r.t time we get its acceleration        a(t)=dtd[v(t)]=2×(2t+3)22=(2t+3)24    m/s2
   at=10s=(2×10+3)24=5294   m/

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