Tag: science & technology

The Goldman Environmental Prize (often called Goldman Awards) honors grassroots environmental activists for outstanding contributions to protecting the environment. It's the world's largest prize for grassroots environmental activism, recognizing individuals for sustained and important efforts to protect or enhance the natural environment.

The International Olympic Committee (IOC) has been headquartered in Lausanne, Switzerland since 1915. Switzerland's neutrality provided political stability for this international sports governing body.

The first public steam railway opened in England in 1825 (Stockton to Darlington Railway). While earlier wagonways existed, England pioneered steam locomotives on iron rails during the Industrial Revolution.

Average speed = distance/time = 350 km/7 hrs = 50 km/hr. However, the question asks for average VELOCITY, which is a vector quantity requiring both magnitude and direction. Since we don't know the exact direction between Bangalore and Chennai, we cannot determine the average velocity. Also, the distance given might not be the straight-line displacement needed for velocity calculation.

Without gravity, a projectile launched at 45° has equal initial horizontal and vertical velocity components (vx = v₀cos45°, vy = v₀sin45°). With no acceleration, both components remain constant and equal, so x = y at all times. This gives x - y = 0 as the equation of the straight-line path in the x-y plane. The motion is linear, not circular, and x + y = 0 would mean x = -y, which is incorrect.

In uniform circular motion, acceleration is centripetal - it always points toward the center of the circular path. This acceleration is responsible for continuously changing the direction of velocity to maintain circular motion, not the tangent (which would be the velocity direction).

In circular motion, linear velocity v equals radius r multiplied by angular velocity w (v = rw). This relationship holds because angular velocity w is defined as the rate of change of angle, and the arc length traveled is r times the angle.

Newton's first law states that an object at rest stays at rest AND an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. A moving body with no net force will continue moving at constant velocity, not come to rest.

Friction is a non-conservative force because the work done against friction depends on the path taken - a longer path means more work is lost to friction. In contrast, conservative forces like gravity and electric force have work done that is independent of the path, depending only on initial and final positions.

After 15 minutes, exactly 3 half-lives have passed (15/5 = 3). Each half-life reduces the amount by half, so after 3 half-lives: 1 gram * (1/2)^3 = 1 * 1/8 = 0.125 gram remains.