The function s=f(t) gives the postion of a body moving on a cooridinate line, wi

Question

The function s=f(t) gives the postion of a body moving on a cooridinate line, with s in meters and t in seconds, for given time interval. Use s(t) to find the indicated quantities.

9) s = 4t^2 + 2t + 4, 0 less than or equal to t and t less than or equal to 2

Find the body's displacment and average velocity for the given time interval.

A) The displacement is 20 m. The average velocity is 20 m/sec.

B) The displacement is 20 m. The average velocity is 10 m/sec.

C) The displacement is 12 m. The average velocity is 18 m/sec.

D) The displacement is 28 m. The average velocity is 14 m/sec.

Explanation / Answer

given equation is ,s=4t2+2t+4, 0-<t-<2.---------------->1

       we get,diplacement on substituting,t=2 in eq.1.

                       :.s=4(2*2)+2(2)+4.

                           =24m.

substitute,t=0sec,

s=4m.

:.s=24-4=20m.

         diferentiate eq.1. we get.velocity.

                  ds/dt=8t+2.

                sub,t=2sec.

                  ds/dt=8(2)+2.

                          =18m/sec.

sub,t=0sec.

ds/dt=2m/sec.

:.ds/dt=18-2=16m/sec.

ans:b.

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