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2.Motion in Straight Line
medium
The displacement of a particle moving in a straight line depends on time as $x=\alpha t^3+\beta t^2+\gamma t+\delta$.The ratio of initial acceleration to its initial velocity depends
Aonly on $\alpha$ and $\gamma$
Bonly on $\beta$ and $\gamma$
Conly on $\alpha$ and $\beta$
Donly on $\alpha$
Solution
(b)
$v=3 \alpha t^2+2 \beta t+\gamma$
$v_{t=0}=v_i=\gamma$
$a=6 \alpha t+2 \beta: a_{t=0}=a_i=2 \beta$
$\therefore \frac{v_i}{a_i}=\frac{\gamma}{2 \beta}$
$v=3 \alpha t^2+2 \beta t+\gamma$
$v_{t=0}=v_i=\gamma$
$a=6 \alpha t+2 \beta: a_{t=0}=a_i=2 \beta$
$\therefore \frac{v_i}{a_i}=\frac{\gamma}{2 \beta}$
Standard 11
Physics
