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Right ANSWER is (a) 3 m from A

The BEST I can explain: Relative displacement of B with RESPECT to A = Displacement of B -Displacement of A. On solving we get, relative displacement = 3 m. Hence B is placed at a distance of 3 m from A.

The CORRECT choice is (a) 54

For explanation I would SAY: The formula for CONVERSION is, km/h = (18/5) x m/s. Therefore, 15 m/s = 15 x (18/5) = 54 km/h.

Correct CHOICE is (a) Relative VELOCITY > Absolute velocity

To ELABORATE: The formula for relative velocity is, VECTOR VR = Vector VA – Vector VB. When both the VELOCITIES are opposite in direction, the equation becomes VR = VA – (-VB). Hence the magnitudes add up making the relative velocity greater than the absolute velocity of any of the two bodies.

The correct option is (a) 3

To elaborate: In SPACE we require a minimum of 3 variables to DESCRIBE the position of a body, NAMELY X, y, and z (in Cartesian system). There are also systems other than Cartesian Coordinate system to do this LIKE Cylindrical system, Spherical or Radial system.

Correct CHOICE is (a) Average velocity

The explanation is: The average velocity is obtained by dividing total DISPLACEMENT by total time taken. Instantaneous velocity is calculated at an INSTANT and not over a period of time. Speed is distance divided by time. Velocity is said to be uniform when velocity at EVERY instant is equal to the average velocity.

The CORRECT CHOICE is (a) ONE DIMENSIONAL

Easiest explanation: RECTILINEAR motion happens along a straight line. A straight line is one dimensional. Hence, rectilinear motion is one dimensional.

Correct CHOICE is (a) Absolute

To elaborate: The motion with respect to a stationary frame is CALLED absolute motion. RELATIVE motion is with respect to a moving frame of reference.

Right choice is (c) CONSTANT force

Explanation: SINCE the body is ACCELERATED, the speed and velocity will vary. Momentum DEPENDS on velocity; hence the momentum will also vary. The force remains constant as F = ma.

Right ANSWER is (B) v = x/t

Explanation: The correct formula is v = x/t. Average velocity is total change in displacement divided by total change in TIME. v = dx/dt is the formula for INSTANTANEOUS velocity.

The correct ANSWER is (a) 10 units

Explanation: The DISPLACEMENT is the distance between the FINAL and the INITIAL location. Here the final location is C and the initial is A. We can solve this by USING distance between two points method. AC = Square root ((8^2 – 0^2) + (6^2 – 0^2)) = Square root (100) = 10 units.

Correct answer is (b) 20m

Best explanation: Here we will use the third EQUATION of motion. The third equation of motion is V^2 = u^2 + 2as. At the MAXIMUM height, the velocity of the ball will be zero, THEREFORE, v = 0, u = 20, and a = -g = -10. On solving, we will get s = 20m.

The correct option is (b) 35 units

Explanation: The displacement covered in the first five seconds can be obtained by putting t = 5 in the EQUATION. Therefore, X = 5^5 + 2(5) = 25 + 10 = 35. Hence the answer is 35 units.

Right CHOICE is (a) Velocity

To explain: The gradient or SLOPE of any graph TELLS us the value of its DIFFERENTIAL at that point. Since acceleration is the differential of velocity with respect to time, the gradient is equal to the acceleration.

Correct OPTION is (B) 15m/s

To elaborate: Here we will use the formula for relative velocity, Vector VR = Vector VA – Vector VB. Since both the bodies are MOVING in the same direction, the velocity vectors are of the same sign. VR = 5, VB = 10, therefore, VA = 15m/s.

Right answer is (a) 2

To elaborate: The FUNCTION for velocity can be DERIVED by differentiating the equation with respect to t. v = 2(t-4) is the required function. When t = 5, v = 2(5-4) = 2.

The correct OPTION is (a) 5m/s

For explanation: The absolute velocity of the small block is the same as that of the block moving with 5m/s. This is because absolute velocity is STUDIED with respect to the ground FRAME. The relative velocity of the small block with respect to the other block is zero.

Correct answer is (b) 4

Best explanation: The total change in DISPLACEMENT = 20 m. Total TIME taken = 5 s. Average velocity = total change in displacement/total time taken = 20/5 = 4 m/s.

The CORRECT answer is (d) Speed

Explanation: The distance depends on the final and initial points as these points DEFINE the PATH. Distance also depends on the path chosen, the distance between same initial and final point with DIFFERENT paths can be different. It does not depend on speed as whatever the speed MAY be, if the initial and final points and path remains same, the distance remains same.

Correct ANSWER is (a) 35 units

Easy explanation: In one turn the person covers 5 – (-2) units of distance, i.e. 7. THEREFORE in 5 turns, he will cover 5 X 7 = 35 units of distance.

Right OPTION is (a) 40 m/s FASTER

Easy explanation: Here we need to find the relative velocity of the TRAIN with respect to the truck is VR = VA-VB, VB = 40, VA = 80. On SOLVING we get, VR = 40 m/s. Hence the train will MOVE faster by 40 m/s.

The correct option is (a) 1

To explain I would SAY: There are PRIMARILY 3 equations of motion. These are v = u + at, s = ut + (1/2)at^2 and v^2 = u^2 + 2as.

Right OPTION is (c) 60 m/s^2 Eastwards

The best explanation: Deceleration ALWAYS acts in the direction opposite to the direction of MOTION. MAGNITUDE of deceleration is 60 m/s^2 and it acts in the direction opposite to North. Hence the ANSWER is 60 m/s^2 Southwards.

The correct option is (B) 3

To explain: In uniformly ACCELERATED motion, at least THREE variables are required to completely define the system This can ALSO be found out by using the equations of motion. For finding out the value of any variable, we need at least three known QUANTITIES.

The correct choice is (c) Halfway through the whole trajectory

To explain: When the BALL rises up, there will be a point where it will be in the state of INSTANTANEOUS rest. At the this position the speed of the ball will be 0. Speed is maximum at the INITIAL and final points.

Correct option is (a) 50 km/hr

Easy EXPLANATION: Average speed is defined as TOTAL distance DIVIDED by total time. The total distance is 150 km and total time taken is 3 Hrs, therefore average speed = 150/3 = 50 km/hr.

Right answer is (b) Motion

For explanation: The BODY moves in the state of motion. HENCE it has a VELOCITY and so KINETIC energy. Kinetic energy = (1/2)mv^2.

Right answer is (a) 102

The explanation: ACCELERATION = dv/dt. To find the acceleration, we can DIFFERENTIATE the VELOCITY EQUATION with respect to time. a = 2 + 10t. On putting, t = 10, we get a = 102.

Right choice is (c) SPHERICAL

Explanation: In Spherical system, distance from the CENTER, the angle with the X axis, and the angle with the Z axis are used to define the POSITION of a point. These are RESPECTIVELY represented by R, θ and ф.

Correct option is (b) Acceleration

The best I can explain: The RATE of CHANGE of displacement of a BODY is VELOCITY. The rate of change of rate of displacement of a body, or rate of change of velocity is acceleration.

The correct choice is (a) 2

Easy explanation: Use the SECOND EQUATION of MOTION to FIND the acceleration. s = ut + (1/2)at^2, u = 0, t =15, s=15, therefore, a = 2/15 m/min^2. Now use the first equation to find the final velocity. v = u + at, u = 0, t = 15 min, a = 2/15, therefore, v = 2 m/min.

Correct option is (a) 2 m/h

Explanation: We can USE the FIRST equation of motion here. The first equation says, v = u + at, here, u = 1 m/h, t = 10 Hrs, a = 0.1 m/h^2. On PUTTING all the values in the equation, we will GET v = 2 m/h.

Right answer is (a) 0.1 m/s^2

The best I can explain: Assuming the BALL FALLS with zero initial velocity, then according to the second equation of MOTION, s = ut + (1/2)at^2 = (1/2)at^2. When we put t = 10S, we GET a = 0.1 m/s^2.

Correct answer is (a) It increases with time

For EXPLANATION I WOULD say: This type of motion can be called circular motion with INCREASING radius. As the radius increases, the TANGENTIAL velocity increases (v = RW). Now, as there is only one velocity present, the speed will be equal to the magnitude of the tangential velocity.

Right choice is (a) The shortest PATH

To ELABORATE: Displacement between TWO points is the shortest path between them. It is always LESS than or equal to the distance between them. Displacement can never be greater than distance.

The CORRECT CHOICE is (a) RECTILINEAR

To explain I would say: The HANDS of a clock move in a CIRCULAR manner. Hence, the motion exhibited is circular motion. Moreover, it happens periodically, so it is also periodic motion. But its is not rectilinear motion.

Right answer is (a) Rectilinear

Easiest EXPLANATION: The MOTION of a car on straight ROAD is happening ALONG a straight line. Hence the motion can be CALLED rectilinear as rectilinear motion happens along a straight line. Rest all are non rectilinear motions.

The correct choice is (a) VELOCITY of A with respect to B

To explain I would say: The formula for RELATIVE velocity is, Vector VR = Vector VA – Vector VB. The velocity of A is greater in magnitude hence the relative velocity of A will be positive. The DIRECTION of the relative velocity will be Northwards.

Right ANSWER is (b) 350

The EXPLANATION is: APPLY the first EQUATION of motion in both the parts. For first part, v1 = u + a1t1 = 0 + 5×10 = 50 m/s. For second part, v2 = u2 (= v1) + a2t2 = 50 + 15×20 = 350 m/s.

The correct OPTION is (a) 5sin(5t)

Explanation: Acceleration = dv/dt = d^2x/dt^2. The velocity (V) can be expressed as, v = dx/dt = 5cos(5t). Hence acceleration (a) BECOMES, a = dv/dt = -25sin(5t).

Correct answer is (a) DECELERATION

Easy explanation: Negative acceleration is KNOWN is deceleration. Negative acceleration ACTS in the direction opposite to the direction of MOTION. It is also known as retardation.

The correct choice is (C) It remains constant

To explain: When the BODY is moving with terminal VELOCITY, the velocity does not change. It means that EQUAL displacement is being covered in equal time intervals. Hence the AVERAGE velocity remains constant.

Right answer is (a) 17.14 m/s

Best explanation: Average speed is the total distance divided by total TIME taken. Total DISPLACEMENT (d = VT) = 20×20 + 15×10 + 10×5 = 600 m. Total time = 20 + 10 + 5 = 35 s. THEREFORE, average speed = 600/35 = 17.14 m/s.

Correct answer is (a) 10 m/s

To explain: From FIRST equation of motion we have, v = u + at, which implies that a = 5 m/s^2. From second equation of motion we have s = ut + (1/2)at^2, which implies that s = 40 m. Average SPEED = s/t = 40/4 = 10 m/s.