The motion of a particle is given by the equation The value of the acceleration of the particle at t = 1 s is :
1. | 10 m/s2 | 2. | 32 m/s2 |
3. | 23 m/s2 | 4. | 16 m/s2 |
The displacement \(x\) of a particle varies with time \(t\) as \(x = ae^{-\alpha t}+ be^{\beta t}\)
, where \(a,\) \(b,\) \(\alpha,\) and \(\beta\) are positive constants. The velocity of the particle will:
1. | \(\alpha\) and \(\beta.\) | be independent of
2. | go on increasing with time. |
3. | \(\alpha=\beta.\) | drop to zero when
4. | go on decreasing with time. |
If a body travels some distance in a given time interval, then for that time interval, its:
1. | Average speed ≥ |Average velocity| |
2. | |Average velocity| ≥ Average speed |
3. | Average speed < |Average velocity| |
4. | |Average velocity| must be equal to average speed. |
A body starts falling from height 'h' and if it travels a distance of h/2 during the last second of motion, then the time of flight is (in seconds):
1.
2.
3.
4.
For a particle, displacement time relation is given by . Its displacement, when its velocity is zero will be:
1. \(2\) m
2. \(4\) m
3. \(0\)
4. none of the above
A particle starts from rest with constant acceleration. The ratio of space-average velocity to the time-average velocity is:
where time-average velocity and space-average velocity, respectively, are defined as follows:
1. | 1/2 | 2. | 3/4 |
3. | 4/3 | 4. | 3/2 |
If a ball is thrown vertically upwards with speed u, the distance covered during the last ‘t’ seconds of its ascent is:
1. ut
2.
3.
4.
A man throws some balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time? (Given g = 9.8 m/s2)
1. More than 19.6 m/s
2. At least 9.8 m/s
3. Any speed less than 19.6 m/s
4. Only with a speed of 19.6 m/s
A car is moving along a straight line, say OP in the figure. It moves from O to P in 18 s and returns from P to Q in 6.0 s. The average velocity and average speed of the car in going from O to P and back to Q respectively are:
1. 10 m/s & 10 m/s
2. 20 m/s & 30 m/s
3. 20 m/s & 20 m/s
4. 10 m/s & 20 m/s
The position of an object moving along \(\mathrm{x}\)-axis is given by \(x=a+bt^2\), where \(a=8.5\) m, \(b=2.5\) and \(t\) is measured in seconds. Its average velocity between \(t=2.0\) s and \(t=4.0\) s is:
1. \(10\) m/s
2. \(15\) m/s
3. \(20\) m/s
4. \(25\) m/s