What is the velocity of a marble after 8 seconds, if it is dropped from a sky scraper?

When we say that the marble was dropped, we simply mean that its initial velocity was 0 m/s. Any object dropped from a height, experiences an acceleration due to Earth's gravity. This acceleration is known as acceleration due to gravity and is denoted as 'g'. The value of acceleration due to gravity is 9.81 m/s^2. Thus, the marble will experience an acceleration equal to acceleration due to gravity.

Using the equation of motion:

v = u + at

where, v is the final velocity, t is time elapsed, u is initial velocity and a is object's acceleration.

Hence, final velocity, after 8 seconds is given as:

v = 0 + (-9.81 m/s^2) x (8 seconds) = - 78.49 m/s

A negative sign is commonly used for denoting the downward velocity direction, since (by convention) upwards is considered a positive direction.