Question

for a particle moving along a straight line, the displacement x varies with time t according to the relation
x=alpha t3 +beeta t2+gamma t+ delta,where alpha ,beeta , gamma and delta are constants. The ratio of its initial acceleration and initial velocity depends
1) only on alpha and beeta
2) only on beeta and gamma
3)only on alpha and gamma
4)only on alpha

Answer 1

v = dx/dt = 3at² + 2bt + c
a = dv/dt = 6at + 2b

intital velocity and acceleration are at t=0
u = c
a° = 2b

ratio is c/2b

thus depends on gamma and beta ie 2nd option