1. Distance and displacement
5B Observing and recording motion Topic overview
Distance and displacement
Distance is a scalar quantity so has a size but no direction.
Displacement is a vector quantity and is the straight line distance and direction ‘as the crow flies’ between the starting point and finishing point. For example:
The distance by car from London to Edinburgh is 660 km.
The displacement of Edinburgh from London is 530 km at a bearing of 338°
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2. Speed 5B Observing and recording motion Topic overview
Speed is distance travelled per second. It is a scalar quantity and so does not have a direction.
The speed of moving objects often varies, e.g. driving a car.
average speed = total distance travelled total time taken
The distance travelled, s, at constant speed, v, in a time, t, is given by:
distance travelled = speed × time
𝑠=𝑣×𝑡
s is measured in m, v is measured in m/s and t is measured in s.
A person might walk at 1.5 m/s, run at 3 m/s and cycle at 6 m/s although this depends on terrain and their fitness.
30 mph (the normal urban speed limit) is about 13 m/s
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3. Velocity 5B Observing and recording motion Topic overview
Velocity is a vector quantity. It is speed in a given direction.
velocity= displacement time
Velocity is measured in m/s plus a direction.
A change of speed or a change of direction is a change of velocity, e.g. motion in a circle might be constant speed but changing direction so is a changing velocity.
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4. Distance-time graphs 5B Observing and recording motion Topic overview
When an object moves in a straight line, its motion can be represented by a distance-time graph, e.g. :
A straight line indicates that the speed is constant in that region.
Speed is calculated from the gradient of the graph.
e.g. in the first 10 s, the speed is =2 m/s .
A steeper gradient indicates a greater speed.
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5. Distance-time graphs 5B Observing and recording motion Topic overview
If the speed is not constant, the graph will be a curve rather than a straight line, e.g. :
In this case the object is accelerating because the gradient is increasing.
Speed at a point (e.g. A) is found by drawing a tangent to the curve at that point.
The gradient of the tangent gives the speed, e.g =3 m/s
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6. Acceleration 5B Observing and recording motion Topic overview
Acceleration, a, is given by change in velocity, ∆𝑣 time taken, 𝑡
𝑎= ∆𝑣 𝑡
Δv is measured in m/s, t is measured in s and a in m/s2.
If an object slows down it is said to be decelerating.
A change of direction, even at constant speed, is a change of velocity and so is acceleration.
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7. Velocity-time graphs 5B Observing and recording motion Topic overview
Motion is usefully shown by a velocity-time graph:
The gradient of a velocity-time graph gives the acceleration.
The area under a velocity-time graph gives the displacement.
The area can be calculated if the acceleration is constant (uniform) or found by counting squares under the graph if the acceleration is changing.
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8. Acceleration 5B Observing and recording motion Topic overview
The initial velocity, u, of an object, its final velocity, v, the acceleration, a, and the distance travelled, s are linked by the equation:
(final velocity) 2 − initial velocity 2 =2×acceleration×distance
𝑣 2 − 𝑢 2 =2×𝑎×𝑠
A car accelerating from rest might reach 15 m/s in 5 s which is an acceleration of 3 m/s2.
An object falling freely near the Earth will accelerate at about 9.8 m/s2.
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9. Terminal velocity 5B Observing and recording motion Topic overview
An object moving through a fluid will experience an opposing force that depends on its shape and velocity.
A falling object will experience this opposing force which will increase until the opposing force is equal to the weight.
The resultant force on the object will then be zero and the object falls at a constant speed called the terminal velocity.
A sky-diver reaches terminal velocity when free-falling and with the parachute open.
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10. Newton’s first law 5B Observing and recording motion Topic overview
If there are balanced forces on an object, the resultant force on it are zero and it will not accelerate.
This means that it will remain stationary or continue at a steady speed in a straight line (constant velocity).
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11. Newton’s second law 5B Observing and recording motion Topic overview
If there are unbalanced forces on an object, there will be a resultant force on it and it will accelerate.
This means that the object will change its speed or direction of travel.
The acceleration, a, is directly proportional to the resultant force, F, acting on the object.
The acceleration, a, is inversely proportional to the mass, m, of the object.
resultant force=mass × acceleration
𝐹=𝑚×𝑎
m is measured in kg, a is measured in m/s2 and F is measured in N
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12. Inertia 5B Observing and recording motion Topic overview
The tendency for objects to remain at rest or at a constant velocity is called inertia.
Inertial mass is a measure of the difficulty in accelerating an object.
Inertial mass= 𝐹 𝑎
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13. Newton’s third law 5B Observing and recording motion Topic overview
Every force has an equal and opposite pair.
The forces must:
act on different objects
be of the same type, e.g. gravitational, contact, etc.
act along the same line in opposite directions.
For example:
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14. Stopping distance 5B Observing and recording motion Topic overview
When driving, the stopping distance is the distance travelled by a car between the time a driver sees a hazard and the time the car is at rest.
stopping distance=thinking distance+braking distance
Thinking distance is the distance travelled by the car at constant speed between the driver seeing the hazard and applying the brakes.
The thinking distance is caused by the driver’s reaction time which can vary considerably but is normally about 0.7 s.
The braking distance is the distance travelled by the car as it decelerates once the brakes are applied.
The braking distance varies and depends on a number of factors.
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15. Reaction time 5B Observing and recording motion Topic overview
Reaction times are longer if the driver:
has been drinking alcohol.
has been taking certain drugs. Some bought or prescribed medicines can increase reaction times as do illegal drugs.
is distracted. For example, using a phone, adjusting the radio or music player or not paying attention, are all distractions.
A longer reaction time means a greater thinking distance.
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16. Braking distance 5B Observing and recording motion Topic overview
Adverse road conditions, e.g. water, snow or ice will increase the braking distance.
Poor vehicle condition, e.g. worn tyres or worn/faulty brakes will also increase the braking distance.
The braking distance depends on the speed of the vehicle.
The greater the speed, the greater the force needed to stop the car in a certain distance.
When the brakes are applied, work is done by the frictional force in the brakes. Energy is transferred from kinetic energy and the temperature of the brakes increases.
The greater the speed of the car, the more work has to be done by the brakes and the hotter they will become.
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17. Momentum 5B Observing and recording motion Topic overview
Momentum is a property of all moving objects.
Momentum, p, is the product of mass, m, and velocity, v.
𝑝=𝑚×𝑣
If m is measured in kg and v in m/s then p is measured in kg m/s
Since velocity is a vector quantity, so is momentum.
In a closed system, momentum is conserved so that the total momentum before an event, e.g. a collision, is equal to the total momentum after the event.
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18. Conservation of momentum
5B Observing and recording motion Topic overview
Conservation of momentum
A closed system is one in which no external forces act on the objects. Objects colliding or exploding are a closed system.
In these cases, the total momentum before the collision or explosion is equal to the total momentum after the collision or explosion.
Since momentum is a vector the direction of the momentum has to be taken into account.
The velocity of an object after a collision or explosion can be calculated using conservation of momentum.
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19. Rate of change of momentum
5B Observing and recording motion Topic overview
Rate of change of momentum
Recall that 𝐹=𝑚×𝑎 and also that 𝑎= ∆𝑉 𝑡
Combining these two equations gives:
𝐹=𝑚× ∆𝑣 𝑡 = 𝑚×∆𝑣 𝑡
𝑚×∆𝑣 is change of momentum, Δp.
𝐹= ∆𝑝 𝑡
where t is the time taken to change the momentum.
Thus force is equal to the rate of change of momentum, ∆𝑝 𝑡 .
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20. Changes of momentum 5B Observing and recording motion Topic overview
Since 𝐹= 𝑚×∆𝑣 𝑡 , an increase in the time taken for a given change of momentum to occur will decrease the force.
This is why, for example:
Cars have crumple zones, air bags are fitted and seat belts stretch so that, in the event of a collision, the time taken to stop is increased so decreasing the forces on the occupants of the car and reducing injury.
When catching a ball, the catcher moves their hands back with the ball to increase the time taken to stop the ball and decrease the force on their hands.
When someone jumps, they bend their legs on landing in order to increase the time of landing and so decreasing the force on their bones and joints.
Crash mats are used in gyms and rubberised surfaces in playgrounds so that the time to stop on landing is increased, so decreasing force.
Cycle helmets are designed to deform slowly on impact, so reducing the force.
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