(d) The instantaneous acceleration of the earth points towards the sun.
Explanation:
Since during the mentioned period in (a) and (b) the earth covers a semi circle and there is a displacement between original point to final point, so average velocity can not be zero.
Acceleration is the rate of change of velocity, here the change in velocity may be 30-(-30)=60 km/s but the time taken is six months i.e. 181*24*60*60 s. Dividing the change in velocity by this time will give the quotient much much less than 60 km/s².
Since the earth moves with a constant speed of 30 km/s, so average speed will also be 30 km/s not zero.
Since it is a case of uniform circular motion, the tangential component of the instantaneous acceleration will be zero and only radial component will be there which is directed towards the center (Sun in this case). Only option (d) is correct.
