1. Tardigrade
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  3. Physics
  4. An auto travelling along a straight road increases its speed from 30.0 m s-1 to 50.0 m s-1 in a distance of 180 m. If the acceleration is constant, how much time elapses while the auto moves this distance ?

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Q. An auto travelling along a straight road increases its speed from $30.0\, m \,s^{-1}$ to $50.0 \,m \,s^{-1}$ in a distance of $180 \,m$. If the acceleration is constant, how much time elapses while the auto moves this distance ?

Motion in a Straight Line

Solution:

Let a be constant acceleration of auto.
Here, $u = 30 \,m\, s^{-1}$, $v = 50 \,m \,s^{-1}$, $S = 180 \,m$
As $v^2-u^2=2aS$
$\left(50\right)^{2}-\left(30\right)^{2}=2\times a\times 180$
$\therefore a=\frac{1600}{2\times180}=\frac{40}{9} m\,s^{-2}$
As $S=ut+\frac{1}{2} at^{2}$
$\Rightarrow 180=30\times t+\frac{1}{2}\times\frac{40}{9}\times t^{2}$
$\Rightarrow 2t^{2}+27t-162=0$
Solving this quadratic equation by quadratic formula, we get
$= 4.5\ s$, $- 18 \,s$, ($t$ can’t be negative)
$\therefore . t = 4.5 \,s$