Final answer:
To calculate the total distance the 12 kg block slid down the slope, one must first calculate the block's acceleration due to gravity's component along the slope and then apply it to the kinematic equation for linear motion with constant acceleration.
Step-by-step explanation:
The question asks about the total distance a 12 kg block slides down a frictionless slope that is inclined at a 31-degree angle when given the time of slide is 1.51s. To find the distance, we must first calculate the acceleration of the block down the slope using Newton's second law and the kinematic equations.
The block's acceleration a can be found using a = g × sin(θ), where g is the acceleration due to gravity (approximately 9.81 m/s²) and θ is the angle of the incline. For a 31-degree slope, a = 9.81 × sin(31°).
Next, we'll use the kinematic equation s = ut + 1/2at², where s is the distance, u is the initial velocity (which is 0 since the block starts from rest), a is the acceleration, and t is the time. Plugging in our values, we get s = 0 × 1.51 + 1/2 × a × (1.51)². After finding a, substitute it into the equation to get the distance s.