The velocity-time graph of a particle in one-dimensional motion is shown in the figure. Which of the following formulae is correct for describing the motion of the particle over the time interval to ?
1. | \(x\left(t_2\right)=x\left(t_1\right)+v\left(t_1\right)\left(t_2-t_1\right)+\left(\frac{1}{2}\right) a\left(t_2-t_1\right)^2\) |
2. | \(\mathrm{v}\left(\mathrm{t}_2\right)=\mathrm{v}\left(\mathrm{t}_1\right)+\mathrm{a}\left(\mathrm{t}_2-\mathrm{t}_1\right)\) |
3. | \(\small{x\left(t_2\right)=x\left(t_1\right)+v_{\text {average }}\left(t_2-t_1\right)+\left(\frac{1}{2}\right) a_{\text {average }}\left(t_2-t_1\right)^2\small}\) |
4. | \(\mathrm{v}_{\text {average }}=\left(\mathrm{x}\left(\mathrm{t}_2\right)-\mathrm{x}\left(\mathrm{t}_1\right)\right) /\left(\mathrm{t}_2-\mathrm{t}_1\right)\) |
The figure gives the x-t plot of a particle executing a one-dimensional simple harmonic motion. Then the signs of position & velocity variables of the particle at t = -1.2 sec respectively are:
The position-time \((x\text-t)\) graphs for two children \(A\) and \(B\) returning from their school \(O\) to their homes \(P\) and \(Q\) respectively are shown in the graph. Choose the incorrect statement.
1. | \(B\) reaches home faster than \(A.\) |
2. | \(B\) overtakes \(A\) on the road twice. |
3. | \(B\) walks faster than \(A.\) |
4. | \(A\) lives closer to the school than \(B.\) |
A jet airplane travelling at the speed of \(500~\text{km/h}\) ejects its products of combustion at the speed of \(1500~\text{km/h}\) relative to the jet plane. What is the speed of the latter with respect to an observer on the ground?
1. \(1000~\text{km/h}\)
2. \(500~\text{km/h}\)
3. \(1500~\text{km/h}\)
4. \(2000~\text{km/h}\)
A car moving along a straight highway with a speed of \(126\) km/h is brought to a stop within a distance of \(200\) m. How long does it take for the car to stop?
1. | \(10.2\) s | 2. | \(9.6\) s |
3. | \(11.4\) s | 4. | \(6.7\) s |
Two trains A and B of length \(400\) m each are moving on two parallel tracks with a uniform speed of \(72\) km/h in the same direction with A ahead of B. The driver of B decides to overtake A and accelerates by \(1\) m/s2. If after \(50\) s, the guard of B just brushes past the driver of A, what was the original distance between them?
1. \(2000\) m
2. \(2250\) m
3. \(1200\) m
4. \(1250\) m
On a two-lane road, car A is travelling at a speed of \(36\) kmh–1. Two cars B and C approach car A in opposite directions with a speed of \(54\) kmh–1 each. At a certain instant, when the distance AB is equal to AC, both being \(1\) km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident?
1. \(1\) ms–2
2. \(5\) ms–2
3. \(2\) ms–2
4. \(3\) ms–2
A player throws a ball upwards with an initial speed of . What is the direction of acceleration during the upward motion of the ball?
1. | vertically downwards |
2. | vertically upwards |
3. | first upwards then downwards |
4. | none of the above |
A particle in one-dimensional motion:
1. | with zero speed at an instant may have non-zero acceleration at that instant. |
2. | with zero speed may have non-zero velocity. |
3. | with constant speed, must have non-zero acceleration. |
4. | with a positive value of acceleration must be speeding up. |
A man walks on a straight road from his home to a market \(2.5\) km away with a speed of \(5\) km/h. Finding the market closed, he instantly turns and walks back home with a speed of \(7.5\) km/h. What is the magnitude of the average velocity of the man over the interval of time \(0\) to \(30\) min?
1. \(6\) km/h
2. \(5\) km/h
3. \(5.6\) km/h
4. \(6.6\) km/h