# The equation of a projectile is $$y = ax -bx^{2}$$. Its horizontal range is? 1. $$\frac{a}{b}$$ 2. $$\frac{b}{a}$$ 3. $$a+b$$ 4. $$b-a$$

Subtopic:  Projectile Motion |
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When a particle is projected at some angle to the horizontal, it has a range $$R$$ and time of flight $$t_1$$. If the same particle is projected with the same speed at some other angle to have the same range, its time of flight is $$t_2$$, then:
1. $$t_{1} + t_{2} = \frac{2 R}{g}$$
2. $$t_{1} - t_{2} = \frac{R}{g}$$
3. $$t_{1} t_{2} = \frac{2 R}{g}$$
4. $$t_{1} t_{2} = \frac{R}{g}$$

Subtopic:  Projectile Motion |
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A car is moving at a speed of $$40$$ m/s on a circular track of radius $$400$$ m. This speed is increasing at the rate of $$3$$ m/s2. The acceleration of the car is:
1. $$4$$ m/s2
2. $$7$$ m/s2
3. $$5$$ m/s2
4. $$3$$ m/s2

Subtopic:  Circular Motion |
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The velocity at the maximum height of a projectile is $$\frac{\sqrt{3}}{2}$$ times its initial velocity of projection $$(u)$$. Its range on the horizontal plane is:
1. $$\frac{\sqrt{3} u^{2}}{2 g}$$
2. $$\frac{3 u^{2}}{2 g}$$
3. $$\frac{3 u^{2}}{ g}$$
4. $$\frac{u^{2}}{2 g}$$

Subtopic:  Projectile Motion |
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The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by
$$y =4 t - 2 t^{2}~ \text{m}$$ and $$x =3t$$ metre, where $$t$$ is in seconds and point of projection is taken as the origin. The angle of projection of projectile with vertical is:
1. $$30^{\circ}$$
2. $$37^{\circ}$$
3. $$45^{\circ}$$
4. $$60^{\circ}$$

Subtopic:  Projectile Motion |
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A particle projected from origin moves in the $$x\text-y$$ plane with a velocity $$\overrightarrow{v} = 3 \hat{i} + 6 x \hat{j}$$$\stackrel{}{\mathrm{}}$, where $$\hat i$$ and $$\hat j$$ are the unit vectors along the $$x$$ and $$y\text-$$axis. The equation of path followed by the particle is:
1. $$y=x^2$$
2. $$y=\frac{1}{x^2}$$
3. $$y=2x^2$$
4. $$y=\frac{1}{x}$$

Subtopic:  Speed & Velocity |
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Consider the motion of the tip of the second hand of a clock. In one minute (assuming $$R$$ to be the length of the second hand), its:

 1 displacement is $$2\pi R$$ 2 distance covered is $$2R$$ 3 displacement is zero. 4 distance covered is zero.
Subtopic:  Position & Displacement |
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A particle is moving along a circle such that it completes one revolution in $$40$$ seconds. In $$2$$ minutes $$20$$ seconds, the ratio of $$|displacement| \over distance$$ will be:
1. $$0$$
2. $$\frac{1}{7}$$
3. $$\frac{2}{7}$$
4. $$\frac{1}{11}$$

Subtopic:  Position & Displacement |
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For any arbitrary motion in space, which of the following relations is true?

 1 $$\overrightarrow{v}_{\text {avg }}=\left(\frac{1}{2}\right)\left[\overrightarrow{v}\left(t_1\right)+\overrightarrow{v}\left(t_2\right)\right]$$ 2 $$\overrightarrow{v}(t)=\overrightarrow{v}(0)+\overrightarrow{a} t$$ 3 $$\overrightarrow{r}({t})=\overrightarrow{r}(0)+\overrightarrow{v}(0){t}+\frac{1}{2} \overrightarrow{a}{t}^2$$ 4 $$\overrightarrow{v}_{\text {avg }}=\frac{\left[\overrightarrow{r}\left(t_2\right)-\overrightarrow{r}\left(t_1\right)\right]}{\left(t_2-t_1\right)}$$

Subtopic:  Speed & Velocity |
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A particle starts from the origin at $$t=0$$ sec with a velocity of $$10\hat j~\text{m/s}$$ and moves in the $$x\text-y$$ plane with a constant acceleration of $$(8.0\hat i +2.0 \hat j)~\text{m/s}^2$$. At what time is the $$x\text-$$coordinate of the particle $$16$$ m?

 1 $$2$$ s 2 $$3$$ s 3 $$4$$ s 4 $$1$$ s

Subtopic:  Uniformly Accelerated Motion |
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