Motion in a Straight Line

A particle is moving along $x$-axis with its position (x) varying with time (t) as $x=\alpha t^4+\beta t^2+\gamma t+\delta$. The ratio of its initial velocity to its initial acceleration, respectively, is:

A particle is moving along $x$-axis with its position (x) varying with time (t) as $x=\alpha t^4+\beta t^2+\gamma t+\delta$. The ratio of its initial velocity to its initial acceleration, respectively, is:

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;

[NEET 2025]

When a ruler falls vertically, 5 different persons catch it with different reaction times. (g = 9.8 ms^–2)

A. Person A has reaction time of 0.20 s.
B. Person B has reaction time of 0.22 s.
C. Person C has reaction time of 0.18 s.
D. Person D has reaction time of 0.19 s.
E. Person E has reaction time of 0.21 s.
What is the correct order of the distance travelled by the ruler for each person ?

The speed of light in vacuum is taken as unity. If light takes 6 min 40 s to reach the Earth from the Sun, the distance between the Sun and the Earth in new unit is :

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 $60 \mathrm{km}/\mathrm{h}$ 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.