The velocity at the maximum height of a projectile is times its initial velocity of projection (u). Its range on the horizontal plane is:
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2.
3.
4.
The equation of a projectile is . Its horizontal range is?
1.
2.
3.
4.
When a particle is projected at some angle to the horizontal, it has a range R and time of flight t1. If the same particle is projected with the same speed at some other angle to have the same range, its time of flight is t2, then:
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3.
4.
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
The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by and metre, where t is in seconds and point of projection is taken as the origin. The angle of projection of projectile with vertical is:
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2.
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4.
A particle projected from origin moves in the x-y plane with a velocity , where and are the unit vectors along the x and y-axis. The equation of path followed by the particle is:
1.
2.
3.
4.
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. |
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. 1/7
3. 2/7
4. 1/11
For any arbitrary motion in space, which of the following relations is true?
1. | \(\vec{v}_{\text {avg }}=\left(\frac{1}{2}\right)\left[\vec{v}\left(t_1\right)+\vec{v}\left(t_2\right)\right]\) |
2. | \(\vec{v}(t)=\vec{v}(0)+\vec{a} t\) |
3. | \(\overrightarrow{\mathrm{r}}(\mathrm{t})=\overrightarrow{\mathrm{r}}(0)+\overrightarrow{\mathrm{v}}(0) \mathrm{t}+\frac{1}{2} \overrightarrow{\mathrm{a}} \mathrm{t}^2\) |
4. | \(\vec{v}_{\text {avg }}=\frac{\left[\vec{r}\left(t_2\right)-\vec{r}\left(t_1\right)\right]}{\left(t_2-t_1\right)}\) |
A particle starts from the origin at t = 0 sec with a velocity of and moves in the x-y plane with a constant acceleration of \((8.0\hat i +2.0 \hat j)\) \(\text{ms}^{-2}\). At what time is the x- coordinate of the particle 16 m?
1. | 2 s
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2. | 3 s
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3. | 4 s
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4. | 1 s |