- The velocity of an object is its speed in a particular direction.
- The slope on a velocity-time graph represents the acceleration of an object.
- The distance travelled is equal to the area under a velocity-time graph.
Speed = Distance/Time
Representing motion- speed/time graphs
- The vertical axis of a distance-time graph is the distance travelled from the start.
- The horizontal axis is the time from the start.
- When an object is stationary, the line on the graph is horizontal.
- The steeper the line, the greater the speed of the object.
Representing motion- velocity/time graphs
- The velocity of an object is its speed in a particular direction. This means that two cars travelling at the same speed, but in opposite directions, have different velocities.
- The vertical axis of a velocity-time graph is the velocity of the object.
- The horizontal axis is the time from the start.
- When an object is moving with a constant velocity, the line on the graph is horizontal.
- When an object is moving with a constant acceleration, the line on the graph is straight, but sloped.
- The steeper the line, the greater the acceleration of the object.
- A negative gradient represents an object with a constant deceleration - slowing down.
- The gradient of a velocity-time graph represents the acceleration
- The area under a velocity-time graph represents the distance covered
Acceleration (m/s2) = Change in velocity (m/s)
Time Taken (s)
Forces- Resultant force
- An object may have several different forces acting on it, which can have different strengths and directions. But they can be added together to give the resultant force.
- This is a single force that has the same effect on the object as all the individual forces acting together.
- When all the forces are balanced, the resultant force is zero.
- In diagrams, the longer the arrow (used to represent force), the bigger the force. If the arrows are the same length, so we know they are the same size.
- When all the forces are not balanced, the resultant force is not zero.
- Objects accelerate when the resultant force is not zero.
Size of the force
An object will accelerate in the direction of the resultant force. The bigger the force, the greater the acceleration.
Doubling the size of the (resultant) force doubles the acceleration.
An object will accelerate in the direction of the resultant force. A force on a large mass will accelerate it less than the same force on a smaller mass.
Doubling the mass halves the acceleration.
Resultant FORCE (newton, N) =
mass (kg) × acceleration (m/s2)
Air resistance - drag
- When an object moves through the air, the force of air resistance acts in the opposite direction to the motion.
- Air resistance depends on the shape of the object and its speed.
- Contact force
- This happens when two objects are pushed together.
- They exert equal and opposite forces on each other.
- The contact force from the ground pushes up on your feet even as you stand still. This is the force you feel in your feet. You feel the ground pushing back against your weight pushing down.
Friction and gravity
- This is the force that resists movement between two surfaces which are in contact.
- Friction can be helpful and a nuisance.
- This is the force that pulls objects towards the Earth.
- We call the force of gravity on an object its weight.
- The Earth pulls with a force of about 10 newtons on every kilogram of mass.
Weight and Mass
- Weight is measured in Newtons.
- Mass is measured in kilograms.
- The mass of a given object is the same everywhere, but its weight can change.
Weight (N) = mass (kg) × gravitational field strength (N/kg)
Forces on a FALLING OBJECT
Two forces acting on a falling object are its weight (gravity) and air resistance.
Three stages of falling
When an object is dropped, we can identify three stages before it hits the ground:
- At the start, the object accelerates downwards because of its weight. There is no air resistance. There is a resultant force acting downwards.
- As it gains speed, the object’s weight stays the same, but the air resistance on it increases. There is a resultant force acting downwards.
- Eventually, the object’s weight is balanced by the air resistance. There is NO RESULTANT FORCE and the object reaches a steady speed, called the terminal velocity.
- Work done and energy transferred are measured in joules (J).
- A change in momentum happens when a force is applied to an object that is moving or is able to move. The total momentum in an explosion or collision stays the same.
Work done (joule, J) = force (newton, N) × distance (metre, m)
Gravitational potential energy
Any object that is raised against the force of gravity stores gravitational potential energy. For example, if you lift a book up onto a shelf, you have to do work against the force of gravity. The book has gained gravitational potential energy.
Elastic potential energy
Elastic objects such as elastic bands and squash balls can change their shape. They can be stretched or squashed, but energy is needed to change their shape. This energy is stored in the stretched or squashed object as elastic potential energy.
- Every moving object has kinetic energy (sometimes called movement energy).
- The more mass an object has, and the faster it is moving, the more kinetic energy it has.
The bouncing ball
Several energy transfers happen when a squash ball is dropped onto a table and bounces up again.
When the ball is stationary above the table, its gravitational potential energy (GPE) is at a maximum. It has no kinetic energy (KE), or elastic potential energy (EPE).
As the ball falls, its GPE is transferred to KE and the ball accelerates towards the table.
When the ball hits the table, the KE is transferred to EPE as the ball squashes. As the ball regains its shape, the EPE is transferred to KE and it bounces upwards.
When the ball reaches the top of its travel, all the KE has been transferred to GPE again. Note that the ball will be lower than it was when it was first dropped, because some energy is also transferred as heat and sound to the surroundings.
- A moving object has momentum.
- This is the tendency of the object to keep moving in the same direction.
- It is difficult to change the direction of movement of an object with a lot of momentum.
Momentum (kg m/s) = mass (kg) × velocity (m/s)
Kinetic Energy (equation)
Kinetic energy (J) = 1⁄2 × mass (Kg) × speed2 (m/s)
Force (Equation) when involving momentum!
Force = Change in Momentum
Time taken for change