The coordinates of a moving particle at any time are given by $x = a{t^2}$ and $y = b{t^2}$. The speed of the particle at any moment is
The coordinates of a moving particle at any time are given by $x = a{t^2}$ and $y = b{t^2}$. The speed of the particle at any moment is
- A
$2t(a + b)$
- B
$2t\sqrt {({a^2} - {b^2})} $
- C
$t\,\sqrt {{a^2} + {b^2}} $
- D
$2t\sqrt {({a^2} + {b^2})} $
Similar Questions
A projectile is projected with speed $u$ at an angle $\theta$ with the horizontal. The average velocity of the projectile between the instants it crosses the same level is ............
A projectile is projected with speed $u$ at an angle $\theta$ with the horizontal. The average velocity of the projectile between the instants it crosses the same level is ............
A particle moves with constant speed $v$ along a regular hexagon $ABCDEF$ in the same order. Then the magnitude of the average velocity for its motion from $A$ to
A particle moves with constant speed $v$ along a regular hexagon $ABCDEF$ in the same order. Then the magnitude of the average velocity for its motion from $A$ to
A football is kicked into the air vertically upwards. What is its
$(a)$ acceleration and
$(b)$ velocity at the highest point ?
A football is kicked into the air vertically upwards. What is its
$(a)$ acceleration and
$(b)$ velocity at the highest point ?
A car moves towards north at a speed of $54 \,km / h$ for $1 \,h$. Then it moves eastward with same speed for same duration. The average speed and velocity of car for complete journey is ..........
$List I$ describes four systems, each with two particles $A$ and $B$ in relative motion as shown in figure. $List II$ gives possible magnitudes of then relative velocities (in $ms ^{-1}$ ) at time $t=\frac{\pi}{3} s$.
Which one of the following options is correct?
$List I$ describes four systems, each with two particles $A$ and $B$ in relative motion as shown in figure. $List II$ gives possible magnitudes of then relative velocities (in $ms ^{-1}$ ) at time $t=\frac{\pi}{3} s$.
Which one of the following options is correct?
- [IIT 2022]