Question

A ball is suspended by a cord from the ceiling of a moving motor car.what will be the effect on the position of the ball if the car is moving with (a)uniform velocity(b)an acceleration

Answer 1

It depends on which direction the car is accelerating.
If it is accelerating forwards, the ball will go backwards as it's inertia will resist motion.
If the car is traveling with a constant linear velocity in a circle, then the centripetal acceleration (acceleration towards the center of curvature) will cause the ball to swing towards the side opposite the direction you are turning.
Think of when a car makes a sharp turn and your body moves in the opposite direction, this is because your body wants to keep moving straight but the car is changing direction so your body is pulled to the side it would naturally be going if not for the car turning. This is a type of acceleration even though your speed remains constant.
I'll explain…
Acceleration is by definition the change in velocity per change in time. We can write this as a differential equation
a=dv/dt
Given a function for v we can derivate to find a. Now a and v are both vectors which mean they have a magnitude and direction. What this means as we relate it back to our definition of acceleration is that if there is any change in EITHER the direction OR magnitude of the velocity, there is an acceleration taking place.
By this definition, if the car is:

Speeding up

Slowing down

Turning right

Turning left

Or any combination thereof,

it is accelerating.
If you have a pictorial representation of the way the car is moving, you can do some simple vector subtraction to find the direction of acceleration.
Per Newton’s First Law of physics, an object will remain at rest or in a constant state of linear motion unless acted upon by an external force.
Per Newton’s Second Law we know that
force=mass*acceleration
which tells us that force and acceleration are related by a constant proportionality of mass. With this information we can reason that if the car is accelerating, there must be a force acting on the car to change its direction or speed. Because the ball is not rigidly attached to the car, it experiences a delay in the feeling of the acceleration and is in a constant state of “catching up” to where the the car is while the accelerating force combats the balls inertia as long as the car is constantly accelerating.
Therefore, whichever direction the car accelerates in, the ball will move the opposite direction.
Hope this helped and wasn't too extra.