Physics - Description of Motion in One Dimension
Exam Duration: 45 Mins Total Questions : 30
In the above question the displacement after 4 s from starting point is
- (a)
zero
- (b)
- 40 m
- (c)
+ 20 m
- (d)
+ 40 m
The position of a particle moving in a x - y plane at any instant t is given by x = \(3t^{2}\) - 6t y = \(t^{2}\) - 2t. Select the correct statement :
- (a)
Acceleration is zero at t = 0
- (b)
Velocity is zero at t = 0
- (c)
Velocity is zero at t = 1 s
- (d)
Velocity and acceleration are never zero
A ball is dropped from a bridge 122.5 m above a river. After the ball has been falling for 2s, a second ball is thrown straight down after it. What must its initial velocity be so that both hit the water at the same time?
- (a)
\(26.1\ m/s\)
- (b)
\(29\ m/s\)
- (c)
\(32\ m/s\)
- (d)
\(36\ m/s\)
The velocity of a particle is \(v=v_0+gt+ft^2\). If its positions is x = 0 at \(t=0,\) then its displacement after unit time is
- (a)
\(v_0+2g+3f\)
- (b)
\(v_0+{g\over 2}+{f\over 3}\)
- (c)
\(v_0+g+f\)
- (d)
\(v_0+{g\over 2}+{f}\)
A ball is thrown downwards with velocity v from the top of a tower and it reaches the ground with speed 3v. What is the height of the tower?
- (a)
v2/g
- (b)
2v2/g
- (c)
4v2/g
- (d)
8v2/g
A ball is dropped from the top of a tower 100 m high. Simultaneously another ball is thrown upward with a speed of 50 ms-1. After what time do they cross each other?
- (a)
1 s
- (b)
2 s
- (c)
3 s
- (d)
4 s
Two balls of different masses ma and mb are dropped from two different heights, viz., a and b. The ratio of times taken by the balls to drop through these distances is
- (a)
a : b
- (b)
b : a
- (c)
\(\sqrt { a } :\sqrt { b } \)
- (d)
a2 : b2
The acceleration a (in ms-2) of a body, starting from rest varies with time t (in s) following the equation a = 3t + 4. The velocity of the body at time t = 2s will be:
- (a)
10 ms-1
- (b)
18 ms-1
- (c)
14 ms-1
- (d)
26 ms-1
A block slides down a smooth inclined plane when released from the top, while another falls freely from the same point:
- (a)
sliding block will reach the ground first with greater speed
- (b)
freely falling block will reach the ground first with greater speed
- (c)
both the blocks will reach the ground at the same time but with different speeds
- (d)
both the blocks will reach the ground with same speed but the freely falling block first
The position vector of a particle is, \(\vec { r } =\left( a\cos { \omega t } \right) \hat { i } +\left( a\sin { \omega t } \right) \hat { j } .\) The velocity of the particle is:
- (a)
parallel to position vector
- (b)
perpendicular to position vector
- (c)
directed towards the origin
- (d)
directed away from the origin
A body is dropped from a balloon moving up with a velocity of 4 m s-1when the balloon is at a height of 120.5 m from the ground; the height of the body after five seconds from the ground is:
- (a)
8 m
- (b)
12 m
- (c)
18 m
- (d)
24 m
A man walks in rain with a velocity of 5 km/hour. The raindrops strike at him at an angle of 45° with the horizontal. The downward velocity of the raindrops will be:
- (a)
5 km/h
- (b)
4 km/h
- (c)
3 km/h
- (d)
1 km/h
A particle is projected with velocity vo along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin, i. e., a=∝x2 . The distance at which the particle stop is:
- (a)
\(\sqrt{\frac{3v_0}{2\alpha}}\)
- (b)
\(({\frac{3v_0}{2\alpha}})^{\frac{1}{3}}\)
- (c)
\(\sqrt{\frac{2v_0^2}{3\alpha}}\)
- (d)
\((\frac{3v_0^2}{2\alpha})^{\frac{1}{3}}\)
Two particles start moving from the same point along the same straight line. The first moves with constant velocity v and the second with constant acceleration a. During the time that elapses before the second catches the first, the greatest distance between the particles is:
- (a)
\(\frac{v^2}{a}\)
- (b)
\(\frac{v^2}{2a}\)
- (c)
\(\frac{2v^2}{a}\)
- (d)
\(\frac{v^2}{4a}\)
From a height, 3 balls are thrown with speed u, one vertically upward, second horizontally, third downward with times of fall be t1 , t2 and t3 respectively, then:
- (a)
\(t_2=\frac{t_1+t_3}{2}\)
- (b)
\(t_2=\sqrt{t_1t_3}\)
- (c)
\(t_2=\frac{2t_1t_3}{t_1+t_3}\)
- (d)
none of these
A stone is released from the top of a tower. If its velocity at half of the height is 10 m/s, then height of the tower is: (g = 10m s-2).
- (a)
8 m
- (b)
10 m
- (c)
12 m
- (d)
16 m
A body travelling along a straight line traversed one third of the total distance with a velocity of 4 m/s. The remaining part of the distance was covered with a velocity 2 m/s for half the time and with velocity of 6 m/s for the other half of the time. The mean velocity averaged over the whole time of motion is:
- (a)
5 m/s
- (b)
4 m/s
- (c)
4.5 m/s
- (d)
3.5 m/s
A man throws some balls with the same velocity 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)
- (a)
Equal to 9.8 m/s
- (b)
Equal to 19.6 m/s
- (c)
Less than 19.6 m/s
- (d)
More than 19.6 m/s
If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is:
- (a)
ut
- (b)
\(\frac{1}{2}gt^2\)
- (c)
(u + gt )t
- (d)
\(ut-\frac{1}{2}gt^2\)
A body of mass 1 kg crosses a point O with a velocity of 60 m s-1. A force of 10N directed towards O begins to act on it. It will again cross O in:
- (a)
24 sec
- (b)
12 sec
- (c)
6 sec
- (d)
will never return to O
A point initially at rest moves along x-axis. Its acceleration varies with time as a = (6t + 5) m/s 2. If it starts from origin, the distance covered in 2 s is:
- (a)
20 m
- (b)
18 m
- (c)
16 m
- (d)
25 m
A train accelerated uniformly from rest attains a maximum speed of 40 m/s in 20 sec. It travels at this speed for 20 sec and is brought to rest with uniform retardation in 40 sec. The average velocity during this period is:
- (a)
(80/3) m/s
- (b)
30 m/s
- (c)
25 m/s
- (d)
40 m/s
Two electrons are moving in opposite directions with speeds 0.8 c and 0.4 c, where c is the speed of light in vacuum. Then the relative speed is about:
- (a)
0.4 c
- (b)
0.8 c
- (c)
0.9 c
- (d)
1.2 c
A particle is thrown above, then the correct v-t graph will be:
- (a)
- (b)
- (c)
- (d)
A man of height h walks in a straight path towards a lamp post of height H with uniform velocity u. Then the velocity of the edge of the shadow on the ground will be:
- (a)
\(\frac{hu}{(H-h)}\)
- (b)
\(\frac{Hu}{(H+h)}\)
- (c)
\(\frac{(H-h)}{hu}\)
- (d)
\(\frac{(H+h)}{hu}\)
The distance travelled by a particle starting from rest and moving with an acceleration \(\frac{4}{3}\)ms-2 , in the third second is:
- (a)
\(\frac{10}{3}m\)
- (b)
\(\frac{19}{3}m\)
- (c)
6 m
- (d)
4 m
The area under velocity-time graph for a particle in a given interval of time represents:
- (a)
velocity
- (b)
acceleration
- (c)
work done
- (d)
momentum
- (e)
displacement
A particle is moving eastward with a velocity of 5 m/second. In 10 seconds, the velocity changes to 5 m/second northward. The average acceleration in this time is:
- (a)
zero
- (b)
\(\frac{1}{2}\)m/sec2 towards north-west
- (c)
\(\frac{1}{\sqrt{2}}\)m/sec2 towards north-east
- (d)
\(\frac{1}{2}\) m/sec2 towards north-east