A particle moves in positive x-direction according to law x=12t−t2m. where t time in second. (Take +ve x-axis as +ve).Based on the above facts, answer the following questions.Average velocity from t=0 to t=8 s isAverage speed from t=0 to t = 8 s isAverage acceleration from t= 0s to t= 8s is

Average velocity is defined asvav= Displacement  Time Interval =ΔxΔt=x2−x1t2−t1⇒ vav=12(8)−(8)2−08−0=4ms−1To calculate the average speed, we must first find the instant of reversal of motion, i.e. when v = 0. Sincev=dxdt=12−2t⇒    v=0⇒    t=6sSo distance travelled by the particle from t = 0 to t = 8s isl=|36−0|+|32−36|=40mSo average speed is Average Speed = Total Distance Travelled  Total Time Taken ⇒  Average Speed =408=5ms−1Average acceleration is the rate of change of velocity.v=12-2t t=0, vi=12 t=8, vf=-4 Average acceleration=vf-vi△t=-4-128=-2 ms-2