Question

how can you find the acceleration and velocity of an object moving on an inclined plane

Answer 1

you want to get velocity and acceleration in inclined plane . you definitely about velocity and acceleration that both are vector quantities? and we can write component of any vector quantity along any plane. that's why our teacher teach us resolution of vector. 

mainly we are using component of velocity in case of oblique projectile. 
question says, particle is projected with speed u m/s at an angle \thetaθ with horizontal. 
e.g., $\vec{u}=ucos\theta\hat{i}+usin\theta\hat{j}$
after time t, velocity of particle will be 
$\vec{v}=ucos\theta\hat{i}+(usin\theta-gt)\hat{j}$

actually, I want to say that you should learn resolution of vector. definitely you can understand how to break any vector in inclined plane or along plane.

Answer 2

The velocity and acceleration of the object is given below.

Explanation:

• Suppose an object of mass m is placed on the inclined plane.
• A force will be acting on the object which will be its component of weight.
• The component of weight = mg sinθ

• θ = angle along the inclined plane
• Now let's suppose the object is moving along the inclined plane in the absence of friction.
• F = mgsin θ
• ma = mg sinθ
• a = gsinθ
• Similarly, velocity can be found by using equations of motion.
• S = vt + 1/2 at^2
• 2aS = vf^2 - vi^2
• Vf = Vi + at