Question 1 1 / -0
A bird flies for 4 s with a velocity of |t – 2| m/s in a straight line, where t = time in seconds. It covers a distance of
Question 2 1 / -0
Let velocity and acceleration of a body be denoted by v and a, respectively. Which of the following relations holds true?
Solution
The body which is thrown upwards has zero velocity at the highest point but still has acceleration due to gravity, so option (1) is true.
Question 3 1 / -0
If a particle is moving with uniform velocity, its acceleration is
Solution
When the change in velocity is zero, it means that there is no force acting on the body and hence, no acceleration.
Question 4 1 / -0
A point moves with uniform acceleration and v1 , v2 and v3 denote the average velocities in three successive intervals of time t1 , t2 and t3 . Which of the following relations is correct?
Solution
Let us consider the three successive intervals based on the given data:
For first interval,
Average velocity,
For second interval,
The average velocity,
For third interval:
The average velocity,
Hence, equation (1) - equation (2):
Equation (2) - Equation (3):
Hence, equation (4)/(5):
Question 5 1 / -0
Three particles, A, B and C are thrown from the top of a tower with the same speed. A is thrown straight up, B is thrown straight down and C is thrown horizontally. If they hit the ground with speeds VA , VB and VC, respectively, which of the following relations holds true?
Solution
The sum of kinetic and potential energies will always remain constant. If they have the same height and thrown with the same velocities then, when they hit the ground, their kinetic energy will be same because their potential energies are all zero.A = VB = VC
Question 6 1 / -0
A balloon starts rising from the ground with an acceleration of 1.25 m/s2 . After 8s, a stone is released from the balloon. The stone will
Solution
The velocity of balloon after 8 seconds is,
V = U + at
V = 0 + (1.25) 8
= 10.00 m/s
Initial velocity of stone is 10 m/s upwards
Height reached by balloon =
(Using S = ut +
)
=
= 40 m
Hence, option 4 is correct.
Question 7 1 / -0
An electron starting from rest has a velocity that increases linearly with time, i.e. v = Kt, where K = 2 m/s2 . The distance covered in the first 4 sec will be
Solution
v = Kt
v = 2 x 4 = 8 m/s
Question 8 1 / -0
The initial velocity of a particle moving along a straight line is 20 m/s and its retardation is 2 m/s2 . The distance moved by the particle in the fifth second of its motion is
Solution
Initial velocity u = 20 m/s
a = - 2 m/s
2 Distance moved in 5
th second = Distance covered in 5 seconds - Distance covered in 4 seconds
= S
5 - S
4 S = ut -
S
5 = 20(5) -
2(5)
2 S
4 = 20(4) -
S
5 - S
4 = 20 -
= 20 - 25 + 16
= 11 m
Question 9 1 / -0
A car is moving along a straight road with a uniform acceleration. It passes through two points P and Q with velocities 30 km/hr and 40 km/hr, respectively. The velocity of the car midway between P and Q is
Solution
V
1 = 30 km/hr V
2 = 40 km/hr
Let acceleration = a km/hr
2 Using, V
2 = V
1 + at
Now, 40 = 30 + at (Here, t is time taken to reach Q from P)
10 = at
a =
S = ut +
= 30 t +
= 30 t + 5 t
= 35 t km
Half of S =
V
2 = u
2 + 2 as
V
2 = (30)
2 +
V
2 = 900 + 350
V =
Answer is 35.35 km/hr which is same as 25
km/hr
Question 10 1 / -0
A car travelling at a speed of 40 km/hr is brought to a halt in 8 m by applying brakes. If the same car is travelling at 60 km/hr, it can be brought to a halt with the same braking force in
Solution
As the braking force is same, acceleration is same. Let distance travelled by the car in the first case be s
1 and the distance travelled in the second case be s
2 .
,
Question 11 1 / -0
Two bodies of different masses say 5 kg and 15 kg are dropped simultaneously from a tower. Which of the following statements is correct?
Solution
Both will reach the ground simultaneously because they will start from rest and fall under the same acceleration of 10 m/s2 (g).
Question 12 1 / -0
If a light and a heavy body are released from the same height in vacuum,
Solution
If a light and a heavy body are released from the same height, then they will fall at the same time if they don`t encounter air resistance.
Question 13 1 / -0
The relative velocity of car A with respect to car B is 20√2 m/s due north-east. The velocity of car B is 20 m/s due south. The relative velocity of car C with respect to car A is 20 m/s due north. The speed of car C and the direction (in terms of the angle it makes with the east) is:
Question 14 1 / -0
Two particles are projected simultaneously in the same vertical plane from the same point, but with different speeds and at different angles to the horizontal. The path followed by one as seen by the other is:
Solution
A straight line making a constant angle with the horizontal is the correct option.
Question 15 1 / -0
A swimmer crosses a flowing stream of width b to and fro in time T1 . The time taken to cover the same distance up and down the stream is T2 . If T3 is the time that the swimmer takes to swim a distance 2b in still water, then
Solution
Let's consider that the speed of swimmer in still water is x and the speed of stream flow is y.
Hence, time taken by the swimmer to cross the stream to and fro along the shortest root,
Time taken to swim up and down the stream,
Time taken to travel the distance in still water,
By multiplying equations (2) and (3),
Question 16 1 / -0
A 200 m long train is moving northwards at a speed of 20 m/s. A parrot flying towards south with a speed of 5 m/s crosses the train. The time taken by the parrot to cross the train will be
Solution
Length of train = 200 m
Speed of train = 20 m/s
Parrot's speed = 5 m/s
Relative speed = 25 m/s
Time taken by parrot to cross the train =
= 8 seconds
Question 17 1 / -0
A steam boat goes across a lake and comes back (i) on a quiet day when the water is still, and (ii) on a rough day when there is a uniform current so as to help the journey onward and to impede the journey back. If the speed of the launch, on both days, was same, the time required for the complete journey on the rough day, as compared to that on the quiet day, will be
Solution
Let the speed of current be = y km/hr and speed of boat in still water = x km/hr
Let length across the lobe be = d
Distance travelled along a journey = 2d
(i) On a quiet day time taken across the lake =T
Then,
T =
â¦â¦.. (1)
(ii) On a rough day time taken across the lake = t
Then,
t =
+
=
=
â¦â¦.. (2)
From (1) and (2),
and
and
Hence, the denominator in (2) is smaller as compared to (1). Therefore, it takes longer time on a rough day.
Question 18 1 / -0
Which of the following graphs represents motion with uniform velocity?
Solution
The slope of s-t graph is velocity and if it`s a straight line inclined with the time axis, then its constant velocity. If it is a straight line parallel to the time axis, then body is at rest.
Question 19 1 / -0
The displacement -time graph for two particles A and B are straight lines inclined at angles of 30° and 60° with the time axis. The ratio of the speeds vA : vB is
Solution
The displacement-time graph for two particles A and B are straight lines inclined at angles 30° and 45°.
The slope of S - T graph is the velocity.
Slope of 1
st graph= tan 30° = 1/
Slope of 2
nd graph= tan 60° =
V
A : V
B =
= 1 : 3
Question 20 1 / -0
A motor is making 1200 RPM. Calculate its angular velocity.
Solution
Q = 1200 RPM
ù =
=
rad/s
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