Final answer:
To find the time and velocity at the bottom of a frictionless inclined plane, apply the equations of uniformly accelerated motion using gravity's component along the incline and the block's initial conditions of starting from rest.
Step-by-step explanation:
The student asks about the time and velocity a block takes to reach the bottom of a frictionless inclined plane, starting from rest. To find the time and velocity, we must apply the equations of motion for uniformly accelerated motion. Because there is no friction, the only force acting on the block is gravity, which can be resolved into components parallel and perpendicular to the incline.
First, determine the acceleration of the block down the incline using the formula a = g × sin(θ), where g is the acceleration due to gravity (9.8 m/s²) and θ is the angle of the incline. Then, use the kinematic equation s = ut + ½ at², where s is the distance down the incline, u is the initial velocity (0 m/s since it starts from rest), t is the time, and a is the acceleration, to solve for time t.
Finally, to determine the velocity at the bottom, use the equation v² = u² + 2as, where v is the final velocity at the bottom. Solve for v to find the velocity the block has when it reaches the bottom of the incline. Examples or additional specifics, such as the incline's angle or distance the block travels, are needed for precise calculations.