A particle moving on a curved path possesses a velocity of 3 m/s towards the north at an instant. After 10 s, it is moving with speed 4 m/s towards the west. The average acceleration of the particle is-
1. | 0.25 , 37° south to east |
2. | 0.25 , 37° west to north |
3. | 0.5 , 37° east to north |
4. | 0.5 , 37° south to west |
A man can row a boat with a speed of 10 kmph in still water. The river flows at 6 kmph. If he crosses the river from one bank to the other along the shortest possible path, time taken to cross the river of width 1 km is:
1. 1/8 h
2. 1/4 h
3. 1/2 h
4. 1 h
A bus is going to the North at a speed of 30 kmph. It makes a 90° left turn without changing the speed. The change in the velocity of the bus is:
1. | 30 kmph towards W |
2. | 30 kmph towards S-W |
3. | 42.4 kmph towards S-W |
4. | 42.4 kmph towards N-W |
Two bullets are fired simultaneously horizontally and at different speeds from the same place. Which bullet will hit the ground first? (Air resistance is neglected)
1. | The faster one |
2. | The slower one |
3. | Depends on masses |
4. | Both will reach simultaneously |
An aeroplane flies \(400\) m north and then \(300\) m west and then flies \(1200\) m upwards. Its net displacement is:
1. | \(1200\) m | 2. | \(1300\) m |
3. | \(1400\) m | 4. | \(1500\) m |
Select the incorrect statement:
1. | It is possible to have \(\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right| = 0 \) and \(\frac{\mathrm{d}|\overrightarrow{\mathrm{v}}|}{\mathrm{dt}} \neq 0 \) |
2. | It is possible to have\(\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right| \neq 0 \) and \(\frac{\mathrm{d}|\overrightarrow{\mathrm{v}}|}{\mathrm{dt}}=0 .\) |
3. | it is possible to have\(\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right|=0\) and \(\frac{\mathrm{d}|\overrightarrow{\mathrm{v}}|}{\mathrm{dt}}=0 . \) |
4. | It is possible to have \(\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right| \neq 0\) \(\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}} \neq 0 \) |
A particle of mass 2 kg is moving in a circular path with a constant speed of 10 m/s. The change in the magnitude of velocity when a particle travels from P to Q will be: [assume the radius of the circle is 10/]
1. | \(10 \sqrt{3} \) | 2. | \(20 \sqrt{3}\) |
3. | 10 | 4. | 0 |
To the captain of a ship A travelling with velocity km/h, a second ship B appears to have a velocity km/h. What is the true velocity of the ship B?
1.
2.
3.
4. none of these
An object moves at a constant speed along a circular path in a horizontal XY plane with its centre at the origin. When the object is at x = –2 m, its velocity is –(4 m/s). What is the object's acceleration when it is at y = 2 m?
1.
2.
3.
4.
The position of a moving particle at time \(t\) is \(\vec{r}=3\hat{i}+4t^{2}\hat{j}-t^{3}\hat{k}.\) Its displacement during the time interval \(t=1\) s to \(t=3\) s will be:
1. | \(\hat{j}-\hat{k}\) | 2. | \(3\hat{i}-4\hat{j}-\hat{k}\) |
3. | \(9\hat{i}+36\hat{j}-27\hat{k}\) | 4. | \(32\hat{j}-26\hat{k}\) |