A sports car can accelerate uniformaly to a speed of $162$ km/h in 5 sec. Its maximum breaking retardation is $6 m / s^{2}$ . Minimum time in which it can travel 1 km starting from rest and ending at rest in seconds is?

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Solution

By $v = u + a t \Rightarrow 162 \times \frac{5}{18} = a \times 5$
$\Rightarrow a = 9$ m/s
Area under the graph is the displacemet. Threfore,
$1000 = \frac{1}{2} \times t \times v_{0} - (1)$
Applying $v = u + a t$ from 0 to $t_{0}$ sec,
$v_{0} = 9 t_{0} - (2)$
Applying $v = u + a t$ from $t_{0}$ to $t$ sec,
$v_{0} = 6 (t - t_{0}) - (3)$
By (1) (2) & (3),
t = 23.57 s

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A sports car can accelerate uniformaly to a speed of 162 km/h in 5 sec. Its maximum breaking retardation is 6 m/s2. Minimum time in which it can travel 1 km starting from rest and ending at rest in seconds is?

By v=u+at⇒162×518=a×5 ⇒a=9 m/s Area under the graph is the displacemet. Threfore, 1000=12×t×v0−(1) Applying v=u+at from 0 to t0 sec, v0=9t0−(2) Applying v=u+at from t0 to t sec, v0=6(t−t0)−(3) By (1) (2) & (3), t = 23.57 s

A sports car can accelerate uniformaly to a speed of $162$ km/h in 5 sec. Its maximum breaking retardation is $6 m / s^{2}$ . Minimum time in which it can travel 1 km starting from rest and ending at rest in seconds is?