Module 3: Chapter 3 - Motion Flashcards
What is the equation for average speed?
average speed = Δdistance / Δtime
What is distance?
Distance is a scalar quantity and is the length of a route through space
What is displacement?
Displacement is a vector quantity and is the distance in a given direction. It describes the position pf one point in space relative to another
Describe the velocity of a car moving at a constant speed in a circular motion.
Although the car is travelling at a constant speed, it’s velocity is constantly changing as its direction is constantly changing. Therefore the car is constantly accelerating.
What is speed?
Speed is a scalar quantity and is the distance travelled per unit time. It describes the rate of change of distance
What is velocity?
Velocity is a vector quantity and is the displacement travelled per unit time. It describes the rate of change of displacement
What is instantaneous speed?
The speed at a given moment of time
What is acceleration?
The rate of change of velocity
What is a component vector?
One of 2 or more vectors into which another vector can be separated
What are the suvat equations (definition)?
4 Standard equations describing motion under constant acceleration
What are the 4 suvat equations?
- v = u + at
- s = ut + ½ at²
- v² = u² + 2as
- s = ½(u + v)t
What is direction?
A line along which a vector points, given as an angle or a compass point
What is magnitude?
The size or quantity, independent of direction or units
What is a parabola?
The characteristic path followed by an object moving under gravity in a uniform gravitational field
What is a projectile?
An object which is given an inital force and then allowed to move freely under gravity
What the range (of a projectile)?
The horizontal distance from its starting point at which a projectile will land.
What is the resultant vector?
The vector obtained from the sum. of 2 or more vectors
What is trajectory?
The path that an object follows through space, due to the forces that act upon it. Under the influence of gravity, projectiles in freefall will follow a parabolic trajectory
What is a vector equation?
An equation in which both sides of the equation are vectors of equal magnitude and direction
What is deceleration?
The rate at which an object decreases in velocity
Describe the displacement-time graph of an object with a constant velocity
Describe the displacement-time graph of an object with 0 velocity
Describe the displacement-time graph of an accelerating object
Describe the displacement-time graph of a decelerating object
What is the gradient on a displacement-time graph?
The velocity
What is the gradient on a displacement-time graph?
The velocity
What are graphs of motion?
Visual representations of the motion of a body
Draw the velocity-time graph for an object with a constant acceleration
Draw the velocity-time graph for an object moving at a constant velocity
Draw the velocity-time graph for a stationary object
Draw the velocity-time graph for an object with an increasing acceleration
How do you find the displacement using a velocity-time graph?
Find the area under the graph
What is the gradient of a velocity-time graph?
The acceleration
What does the area under an acceleration time graph represent?
The change in velocity
Determine the time at which car P overtakes car Q
8.25 seconds
What is the equation for acceleration?
acceleration = Δvelocity/Δtime
Draw the displacement time graph for a bouncing ball
Draw the velocity time graph for a bouncing ball
Draw the acceleration time graph for a bouncing ball
What does SUVAT stand for?
S - Displacement
U - Initial velocity
V - Final velocity
A - Acceleration
T - Time
What are the 5 SUVAT equations?
- v = u + at
- s = ½(u+v)t
- v² = u² + 2as
- s = ut + ½at²
- s = vt - ½at²
Which SUVAT equation does not contain s?
v = u + at
Which SUVAT equation does not contain a?
s = ½(u+v)t
Which SUVAT equation does not contain t?
v² = u² + 2as
Which SUVAT equation does not contain v?
s = ut + ½at²
Which SUVAT equation does not contain U?
s = vt - ½at²
How is the SUVAT equation “v = u + at” derived?
a = Δv / Δt
a = (v-u) / t
at = v-u
v= u + at
How is the SUVAT equation “s = ut + ½at²” derived?
s = ut + ½(v-u)t
s = ut + ½(at)t
s = ut + ½at²
How is the SUVAT equation “s = ½(u+v)t” derived?
Start with s = ut + ½at²
s = ut + ½at²
s = ut + ½((v-u)/t)t² (substitute a = (v-u)/t)
s = ut + ½(v-u)t
s = ut + ½vt - ½ut
s = ½vt + ½ut
s = ½(v + u)t
How is the SUVAT equation “v² = u² + 2as” derived?
Start with s = ½(v + u)t
s = ½(v + u)t
s = ½(v + u)(v - u)/a (substitute t = (v-u)/a)
2as = (v + u)(v - u)
2as = v² - vu + vu - u²
2as = v² - u²
v² = u² + 2as
What is the most important SUVAT equation and why?
v = u + at as all the other equations can be derived from it
What are the steps for solving a SUVAT equation question?
- State positive and negative directions
- Write out SUVAT and state your values
- Write out the required equation
- Solve
Describe the motion of a skydiver as they jump out of the plane and open their parachute:
At the start of the jump, the air resistance is small and so the skydiver accelerates downwards at 9.81ms⁻². As his velocity increases, his air resistance will increase, causing acceleration to decrease. Eventually the air resistance will be big enough the balance the weight of the skydiver. Therefore the forces on the skydiver are balanced and so he stops accelerating and the velocity remains constant, this is his terminal velocity. When he opens his parachute the air resistance suddenly increases, causing him rapidly decelerate (slow down), as the upward force of air resistance is greater than the downward force of weight. Because he is slowing down the air resistance will decrease until it again balances the weight. At this point the skydiver has reached a new, lower, terminal velocity
Draw the velocity time graph of a skydiver jumping out of plane and opening their parachute on earth and on the moon:
Blue = Earth
Red = Moon
Explain the velocity time graph of a skydiver jumping out of plane and opening their parachute
Blue = on Earth
Red = on The Moon
On Earth:
At the start of the jump, the air resistance is small and so the skydiver accelerates downwards at 9.81ms⁻². As his velocity increases, his air resistance will increase, causing acceleration to decrease. Eventually the air resistance will be big enough the balance the weight of the skydiver. Therefore the forces on the skydiver are balanced and so he stops accelerating and the velocity remains constant, this is his terminal velocity. When he opens his parachute the air resistance suddenly increases, causing him rapidly decelerate (slow down), as the upward force of air resistance is greater than the downward force of weight. Because he is slowing down the air resistance will decrease until it again balances the weight. At this point the skydiver has reached a new, lower, terminal velocity
On the moon:
As the skydiver jumps, they will accelerate towards the ground at a constant rate (1.62 ms⁻²), this acceleration will not change as the skydivers velocity increases or when they open the parachute as there is no atmosphere on the moon, and therefore no air resistance. The acceleration is constant until they collide with the ground
How is air resistance usualy treated in calculations?
It is ignored and treated as negligable, therefore SUVAT equations (which require constant acceleration) can be used for objects in freefall
what is g?
The value of the gravitational field strength on earth (9.81ms⁻²)
What is free fall?
An object is said to be in free fall when it is accelerating under gravity with no other force acting on it
What is the acceleration of free fall denoted by?
g
What are 3 methods for determining g?
- Using an electromagnet and a trapdoor
- Using light gates
- Timing a ball dropping
What is the equation for upthrust?
Upthrust = ρVg
Where, ρ = density of the liquid
V = volume of object submerged
What are the forces acting on an object fully submerged in water?
Upward - Upthrust and Viscous Drag (water resistance)
Downwards - Weight
What is Viscous Drag?
The friction between the fluid and a surface which may be the outside of an object or inside
What is stopping distance?
Stopping distance is how long a vehicle will travel between the moment the driver sees the danger, and when the vehicle comes to a complete stop. Stopping distance = thinking distance + braking distance.
What factors affect thinking distance?
- Level of alertness
- Drugs/alcohol in system
- Distractions in/out of vehicle
- Speed of Vehicle
What factors affect braking distance?
- Mass of vehicle
- Condition of vehicle brakes
- Condition of vehicle tyres
- State of the road (gravel/ice/snow/rain)
- Speed of vehicle
What factor affects both braking distance and thinking distance?
Speed of vehicle
That is the relationship between thinking distance and speed?
Thinking Distance ∝ Speed
What is the realtionship between braking distance and speed?
Braking Distance ∝ Speed²
Prove that: Thinking Distance ∝ Speed
Distance = Speed x Time
Work Done = Force x Distance
Work Done = Force x Speed x Time
Energy Transferred (to bring car to stop) = Force x Speed x Time
Energy Transferred (to bring car to stop) ∝ Speed
Thinking Distance ∝ Speed
Prove that: Braking Distance ∝ Speed²
Kinetic Energy = ½ x Mass x Velocity²
Kinetic Energy = Energy Transferred (to bring car to stop)
Energy Transferred (to bring car to stop) = ½ x Mass x Velocity²
Energy Transferred (to bring car to stop) ∝ Speed²
Braking Distance ∝ Speed²
For a particular car, the braking force is 70% of the weight of the car, show that the braking distance of the car travelling at a speed v, is given by: Braking Distance = 0.073v²
Braking Force = 0.7 Weight
0.7 Weight = 0.7mg
Kinetic Energy = ½ x Mass x Velocity²
Work Done = Force x Distance
Force x Distance = ½ x Mass x Velocity²
0.7mgd = ½mv²
0.7 x 9.81d = ½v²
d = 0.73
What is thinking distance?
The distance travelled between the moment when the driver first sees a reason to stop, to the moment when the driver applies the breaks
What is braking distance?
The distance travelled from the moemnt the brake is applied until the vehicle stops
What is the equation for thinking distance?
Thinking Distance = Reaction Time x Speed
What assumptions are made when calculating with projectile motion?
We assume horizontal motion is not slowed by air resistance, therefore there is no horizontal acceleration or deceleration
How do you solve a projectile motion question?
- Draw a diagram
- Define the positive direction
- List what you have in the horizontal direction
- List what you have in the vertical direction
- Split question into vertical and horizontal components
- Calculate
What is the same of the horizontal and vertical components when calculating projectile motion?
Time
A projectile is launched at an angle of 45° to the horizontal with a velocity of 30 m/s. Calculate the maximum height reached by the ball and the horizontal distance at this height
Vertical = 22.9m
Horizontal = 45.9m
A projectile is launched from the ground at an angle of 30° to the horizontal with a velocity of 20m/s. Calculate the horizontal distance it travels before it hits the ground again
35.3m
A tennis ball is hit horizontally from the top of a building, it takes 4s to reach the ground and lands 80m form the building. What is:
* The height of the building?
* The vertical velocity of the ball just before it hits the ground?
* The horizontal Velocity?
* The resultant velocity and the angle it makes with the ground?
- 78.5m
- -39.2m/s
- 20m/s
- 44m/s, 63° to the horizontal
Why is there no horizontal accleration for a projectile (assuming air resistance is negligable)?
The only force acting upon the object is weight, and since weight has a horizontal component of 0 there is no horizontal acceleration
Explain how a systematic error in each of the measured quantities could have an affect on the gradient of the line
- If there is a systematic error in “s”, there would be no change to the gradient as all points would be increased or decreased by the same amount
- A systematic error in “t” would cause a change in the gradient as although the error in t is constant, “t^2” causes an increased error for each point therefore the gradient changes
Explain how the time it takes for the ball to travel from A to B compares with the time it takes the ball to travel from B to C
The time is the same as for both the vertical distance and vertical acceleration are the same, therefore the time is the same
0.75k
