Answer to Question #4410 in Mechanics | Relativity for Preet

Question

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

Answer 1

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).