Practice free Motion in a Straight Line (Physics) NEET multiple-choice questions online with instant answers and detailed explanations. No login required.
In some appropriate units, time ($t$) and position ($x$) relation of a moving particle is given by $t = x^2 + x$. The acceleration of the particle is:
$\dfrac{dt}{dx} = 2x+1\Rightarrow v = \dfrac{1}{2x+1}$. $a = v\dfrac{dv}{dx} = \dfrac{1}{2x+1}\cdot\left(-\dfrac{2}{(2x+1)^2}\right) = -\dfrac{2}{(2x+1)^3}$.
Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every $T$ min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period $T$ of the bus service and the speed (assumed constant) of the buses.
$\dfrac{vT}{v-60} = 30$, $\dfrac{vT}{v+60} = 10$. Dividing: $\dfrac{v+60}{v-60} = 3\Rightarrow v = 120$ km/h; then $T = 15$ min.
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