Acceleration and Inclined Plane

Acceleration can be both positive and negative, depending on the direction of motion. In this case, the trolley is moving down an inclined plane, which means it is experiencing a positive acceleration.

Acceleration and Retardation

Retardation is a term commonly used to describe negative acceleration or deceleration. When an object slows down or comes to a stop, it is experiencing a negative acceleration or retardation. However, in this scenario, the trolley is not slowing down or coming to a stop. It is accelerating in the downward direction due to the gravitational force acting on it.

Explanation

When an object moves down an inclined plane, its acceleration can be determined using the formula:

a = g * sinθ

where "a" is the acceleration, "g" is the acceleration due to gravity (approximately 9.8 m/s²), and "θ" is the angle of inclination.

In this case, the acceleration is given as 2 cm/s². To convert this into m/s², we divide by 100:

2 cm/s² = 0.02 m/s²

Using the equation above, we can find the angle of inclination:

0.02 = 9.8 * sinθ

sinθ = 0.02 / 9.8

θ = sin⁻¹(0.02 / 9.8)

θ ≈ 0.0129 radians

The trolley's velocity after 3 seconds can be calculated using the equation:

v = u + at

where "v" is the final velocity, "u" is the initial velocity (which is assumed to be 0 in this case), "a" is the acceleration, and "t" is the time.

Substituting the values:

v = 0 + (0.02 m/s²) * (3 s)

v = 0.06 m/s

Therefore, the velocity of the trolley 3 seconds after the start is 0.06 m/s.

In conclusion, the acceleration of the trolley is positive because it is moving down the inclined plane. The acceleration is not considered as retardation because the trolley is not slowing down or coming to a stop. The velocity after 3 seconds can be calculated using the equation v = u + at, where "a" is the acceleration and "t" is the time.