# Archive | M1

## Piecewise Motion

In general the motion of a particle is not smooth. Particles may change direction suddenly, collide, a string may become taut or new forces appear, thus changing the acceleration. In these circumstances, we can define for example, the velocity over certain intervals of time. These points should be noted: The displacement is always continuous. If […]

## Equations for Projectiles

A projectile is a body that falls freely under gravity ie the only force acting on it is gravity. In fact this is never strictly true, since there is always air resistance for example, but these other forces are small compared to gravity in most circumstances so we ignore them. We can resolve the initial […]

## More on Relative Vectors and Velocities

If a particle North or South, East or West of another particle, then we can write down conditions that the position vectors must satisfy. If the particle A is North of particle B thenand If the particle A is East of particle B thenand Suppose then that When A is North of B, the(or) components […]

## Hanging Particles Connected by Pulleys

If two particles of differing masses are connected be a string that passes over a smooth pulley – so there is no friction – as shown below, then the particles will start to move – the heavier particle with massmoving down. We can find the acceleration and tension for each particle in the above system […]

Not all suvat questions can be solved with a single application of the suvat formulae. Sometimes two applications are required, simultaneous equations are formed and these must be solved. A particle starts from rest at a point O. It accelerates uniformly to a pint Pin 2 seconds, at which it has speed u. It continues […]

## Bodies in Equilibrium

When a body is in equilibrium, we can resolve all the forces in any direction, and in each direction we find there are no net forces. If a body has no forces acting on it, it may still move, but it will not accelerate, because by Newton’s second law of motion, F=ma, if F=0, a=0. […]

## Velocity Time Graphs

A velocity time graph is a graph of time on the x axis plotted against velcity on the y axis. Velocity time graphs have two very important features: The area under the graph represents the displacement from the start point. The gradient of the graph at any point is the acceleration at that point. It […]

## Particles on Slopes (1)

There are several things that must be done for every particle that lies on a slope. 1)If you don’t have a diagram, draw one. 2)Do not resolve vertically and horizontally. Resolve perpendicular and parallel to the slope. Remember that the reaction force is always perpendicular to the surface, that gravity always acts downwards, and that […]

## The Principle of Conservation of Momentum

The momentum of a body of mass m moving with velocity v is given by mv. Notice that velocity is used and not speed, so we must take the direction of the body into account. It is useful to form the habit of taking right as positive and left as negative directions respectively – this […]

## Impulse – Newton’s Third Law

If a body receives a push, it’s velocity will increase in the direction of the force. It will accelerate in the direction of the force and will receive an impulse. The impulseis equal to the change in momentum and we can write It is important to take the direction of the velocity into account.. It […]