Question #4410

The velocity of a particle is given by the equation V=4t^2+5.
(a)the average acc b/w the time interval t1=2s and t2=4sec
(b)the instatenous accerlation at t=4 sec

Expert's answer

The velocity of a particle is given by the equation V=4t^2+5.

(a)the average acc b/w the time interval t1=2s and t2=4sec

V'=8t; (time derivative)

a1=8*2=16; (instatenous accerlation at t=2 sec)

a2=8*4=32; (instatenous accerlation at t=4 sec)

A=0.5(a1+a2)=(16+32)/2=24 (the average acc b/w the time interval t1=2s and t2=4sec).

(b)the instatenous accerlation at t=4 sec

V'=8t; (time derivative)

t=4; (current time)

a=8*4=32 (instatenous accerlation at t=4 sec).

(a)the average acc b/w the time interval t1=2s and t2=4sec

V'=8t; (time derivative)

a1=8*2=16; (instatenous accerlation at t=2 sec)

a2=8*4=32; (instatenous accerlation at t=4 sec)

A=0.5(a1+a2)=(16+32)/2=24 (the average acc b/w the time interval t1=2s and t2=4sec).

(b)the instatenous accerlation at t=4 sec

V'=8t; (time derivative)

t=4; (current time)

a=8*4=32 (instatenous accerlation at t=4 sec).

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