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

Question

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?

Smart Achievers · Accepted Answer

(2)

Let $a$ be constant acceleration of auto.

$s^{- 1}$

As $v^{2} - u^{2} = 2 a S$

${(50)}^{2} - {(30)}^{2} = 2 \times a \times 180$ $∴$ $a = \frac{1600}{2 \times 180} = \frac{40}{9} m s^{- 2}$

As $S = u t + \frac{1}{2} a t^{2}$ $\Rightarrow$ $180 = 30 \times t + \frac{1}{2} \times \frac{40}{9} \times t^{2}$

$\Rightarrow$ $2 t^{2} + 27 t - 162 = 0$

Solving this quadratic equation by quadratic formula, we get

$t = 4.5 s, - 18 s$ ( $t$ can't be negative)

$∴$ $t = 4.5 s$

Solution

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

1 6.0 s

2 4.5 s

3 3.6 s

4 7.0 s

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