Collisions, Momentum and Kinetic Energy

Acceleration is the rate of change of velocity, giving the SI unit metre per second squared (m/s²). Newton metre is torque, newton second is impulse (momentum change), and metre per quartic second is not a meaningful physical unit.

The kinetic energy formula is KE = 1/2 mv², where m is mass and v is velocity. The square of velocity is crucial - doubling velocity quadruples kinetic energy, showing why speed matters more than mass in many collision scenarios.

Kinetic energy is the energy of motion, calculated as K = ½mv² (half mass times velocity squared). Option A (mgh) is gravitational potential energy, option C is total mechanical energy, and option D is nonsensical.

The correct formula for kinetic energy is k = (1/2)mv², where m is mass and v is velocity. Option D correctly shows k = (1/2).m.v.v which represents mv². Option A has an extra v (v³), Option B is incomplete (0.5mv), and Option C only has mv (not squared).

Using conservation of momentum: Initial momentum = (2kg × 3m/s) + (1kg × -4m/s) = 6 - 4 = 2 kg m/s. After collision, combined mass = 3kg moving with velocity v. So 3v = 2, giving v = 2/3 m/s. The negative sign for object B's velocity indicates opposite direction.

Using impulse-momentum theorem: impulse J = F × t = Δp = mΔv. When force doubles (2F) and time doubles (2t), impulse becomes 2F × 2t = 4Ft, which is 4 times the original. Since mass is constant, velocity change also increases 4-fold. The 8-fold option incorrectly multiplies only the force, while 2-fold ignores one factor.

Net force = applied force - friction. Friction = μmg = 0.4 × 10 × 9.8 = 39.2N. Applied force = 20N, so friction exceeds applied force. The object won't move, meaning acceleration is 0 m/s². Options B and D come from incorrectly ignoring friction or misapplying the formula.

The pendulum bob's speed at the bottom is given by v = sqrt(2gh). When the height is quadrupled, the speed only doubles (sqrt(4) = 2). In a perfectly elastic collision between objects of equal mass, the bob transfers all its velocity to the block, so the block's initial speed becomes twice as fast.

Einstein's famous equation is E=mc², where E is energy, m is mass, and c is the velocity of light. The speed of light squared (c²) is the conversion factor between mass and energy.

Momentum is defined as the product of an object's mass and its velocity (p = mv). This is a fundamental concept in physics describing the quantity of motion. Energy, Force, and Acceleration are related but distinct quantities - Energy is 1/2 mv^2 for kinetic energy, Force equals mass times acceleration (F=ma), and Acceleration is the rate of velocity change.

In an elastic collision with a wall, the velocity reverses direction but keeps the same magnitude. Momentum changes from +mv to -mv, so Δp = (-mv) - (+mv) = -2mv. The magnitude of impulse is |Δp| = 2mv. Impulse equals change in momentum, not just momentum (mv). Zero would mean no collision, and the answer is determinable.

The gravitational potential energy of a body of mass m at height h above ground level is given by PE = mgh, where g is acceleration due to gravity. This formula represents the work done against gravity to raise the mass to height h. Option A (mg) is weight, option B (m) is just mass, and option C (g) is just gravitational acceleration - none of these are energy.

The potential energy (PE) of an object at height h is given by PE = m × g × h, where m is mass, g is acceleration due to gravity, and h is height. This formula represents the work done against gravity to lift the object. The other options are incorrect: option B resembles kinetic energy formula, options C and D have incorrect mathematical relationships.

From Newton's second law: F = dp/dt, so change in momentum p = F × t. Since both bodies experience the same force for the same time, they acquire the same momentum. Lighter body will have greater velocity and kinetic energy (different acceleration).

Kinetic energy is the one half the mass multiplied by the square of the velocity, K=1/2mv². If mass is doubles, the kinetic energy doubles.