If the velocity v of a particle moving along a straight line decreases linearly with its displacement s from 20 m/s to a value approaching zero at s = 30 m figure, then acceleration of the particle at s = 15 m is

The slope of the line = - 2/3The equation of line is given by(v−20)=−23(s−0)∴v=20−(2/3)sThe velocity at s = 15 m is given byV=dsdts=15m=20−23×15=10m/sThe acceleration can be obtained by differentiating eq. (1) with respect to time, i.e.,a=dvdt=0−23dsdt∴dvdts=15m=−23dsdts=15m=−23×10=−203m/s2