MCQ
A particle moves in a plane with constant acceleration in a direction different from the initial velocity. The path of the particle will be
- AA straight line
- BAn arc of a circle
- ✓A parabola
- DAn ellipse
✓
Answer
Correct option: C.
A parabola
c
(c) A particle moves with constant acceleration in a direction different from initial
(c) A particle moves with constant acceleration in a direction different from initial
velocity. Let the velocity be $v,$ acceleration be $a,$ angle between them is $\theta\left[\theta<90^{0}\right]$
Component of Velocity in the Direction of $a$ is $v \cos \theta$ and in a direction perpendicular to $a$ is vsin $\theta$
From equations of Kinematics, In the direction of acceleration, $y=v \cos \theta t+\frac{1}{2} a t^{2}-----(1)$
In the direction perpendicular to acceleration,
$x=v \sin \theta t$
$t=\frac{x}{v \sin \theta}--------(2)$
Substituting 2 in $1,$ we get:
$y=v \cos \theta\left(\frac{x}{v \sin \theta}\right)+\frac{1}{2} a\left(\frac{x^{2}}{\sin ^{2} \theta}\right)$
$y=\frac{x}{\tan \theta}+\frac{1}{2} a \frac{x^{2}}{\sin ^{2} \theta}$
This is in the form of a parabola: $y=A x^{2}+B x+C$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The displacement of a particle varies according to the relation $x = 3 \sin 100 \, t + 8 \cos ^2 50\,t $. Which of the following is/are correct about this motion .
→The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough. A body starting from the rest at top comes back to rest at the bottom if the coefficient of friction for the lower half is given by
→The equation of a standing wave in a string fixed at both ends is given as $y=2 A \sin k x \cos \omega t$ The amplitude and frequency of a particle vibrating at the mid of an antinode and a node are respectively
→Which of the following statement is true
Graphs below show the entropy versus energy $U$ of two systems $1$ and $2$ at constant volume. The initial energies of the systems are indicated by $U_{1, i}$ and $U_{2, i}$, respectively. Graphs are drawn to the same scale. The systems are then brought into thermal contact with each other. Assume that, at all times the combined energy of the two systems remains constant. Choose the most appropriate option indicating the energies of the two systems and the total entropy after they achieve the equilibrium.
→A ball is thrown on a lawn in such a way that it initially slides with a speed $v_0$ without rolling. It gradually picks up rotation motion. Speed of the ball at which there will be rolling without slipping is
→The angular velocity of a particle rotating in a circular orbit $100$ times per minute is
→A source of sound is moving with constant velocity of $20\, m/s$ emitting a note of frequency $1000 \,Hz.$ The ratio of frequencies observed by a stationary observer while the source is approaching him and after it crosses him will be
→(Speed of sound $v = 340\, m/s$)
The quantities remaining constant in a collisions are
- Momentum, kinetic energy and temperature.
- Momentum and kinetic energy but not temperature.
- Momentum and temperature but not kinetic energy.
- Momentum, but neither kinetic energy nor temperature.
An unloaded bus can be stopped by applying brakes on straight road after covering a distance $x$. Suppose, the passenger add $50 \%$ of its weight as the load and the braking force remains unchanged, how far will the bus go after the application of the brakes? (Velocity of bus in both case is same)
→