Question

The position of an object, moving in one dimensions, is given by the formula x(t) = (4.2t^2 + 2.6)m calculate its (1) average velocity in the time interval from t=0 to t=3s and (2) instantaneous velocity at t=3s (ANSWER IS 12.6M/S, 25.2M/S

Answer 1

average velocity = x2-x1/t2-t1. t2=3sec and t1=0 sec
x2=40.4 and x1= 2.6
average velocity=40.4-2.6/3
and: 12.6m/sec
instantaneous velocity is derivative of distance=8.4t at t=3 8.4×3= 25.2m/sec

Answer 2

here total displacement is 40.4-3.6=37.8
average velocity = total displacement /time = 37.8/3=12.6m/s
by differentiating x w.r.t t we got v=8.4t
v at 3 second = 8.4*3=25.2m/s