As a marble rolls down a hill, it accelerates at 3 m/s^2. If it starts from rest , how far will it have moved after 6 seconds??
distance = 1/2 * acceleration * (time)^2
To find the distance the marble will have moved after 6 seconds, we need to use the equation of motion:
distance = initial velocity × time + (1/2) × acceleration × (time)^2
We know that the initial velocity is 0 m/s since the marble starts from rest. The acceleration is given as 3 m/s^2, and the time is 6 seconds. Plugging these values into the equation, we can calculate the distance:
distance = 0 × 6 + (1/2) × 3 × (6)^2
distance = 0 + (1/2) × 3 × 36
distance = 0 + 1.5 × 36
distance = 54
Therefore, after 6 seconds, the marble will have moved a distance of 54 meters.