3 Motion Flashcards
What is instantaneous speed
Speed over a really short time, tangent of a graph at a particular time
average speed and velocity equation
speed = distance/ time
velocity = displacement/ time
define acceleration
rate of change of velocity m s^-2
properties of a velocity-time graph - gradient, area
Gradient:
- positive - constant acceleration
- zero - constant velocity
negative - constant deceleration
- curve - changing acceleration
area: displacement
Properties of an acceleration-time graph - gradient, area
Gradient:
value for the ‘jerk’ - rate of change of acceleration
Area: change in velocity
Derive v=u+at from a velocity time graph
acceleration=gradient
a=(v-u)/t
rearranging: v=u+at
Derive s=ut+1/2at^2 from a velocity time graph
displacement=area under graph
area = ut + (1/2(v-u)t)
(v-u=at)
s=ut+1/2at^2
Derive s=1/2(u+v)t from a velocity time graph
displacement=area of a trapezium
s=1/2(v+u)t
Derive v^2=u^2+2as from a velocity time graph
v=u+at – t=(v-u)/a
t is substituted into s=1/2(u+v)t
s=1/2(u+v)(v-u/a)
(u+v)(v-u)=2as
v^2-u^2=2as
v^2=u^2+2as
Formula for stopping distance
Thinking + Braking Distance = Stopping Distance
Thinking distance factors and equation
Tiredness, drugs, alcohol, distractions.
Thinking = reaction time x speed
Braking distance factors
Speed of car, road conditions, tyre and brake conditions, weather conditions.
What is the relationship between velocity and stopping distance?
braking distance is proportional to the square of the velocity - Ek=1/2mv^2
Why does the value of g vary on Earth?
depends on factors including altitude, latitude and geology of an area
Practical to determine g? (Electromagnets)
Electromagnet and trapdoor: current switched off, timer is triggered, electromagnet demagnetises and ball falls. Hits trapdoor, contact broken and timer stops.
How to get value for g when plotting graph?
plot distance (y) against time^2 (x).
s=ut+1/2 at^2
Since object dropped from rest and a=g:
s=1/2gt^2
gradient = g/2
Projectile motion - what happens to vertical and horizontal velocities?
Vertical velocity changes due to acceleration of free fall.
Horizontal velocity remains constant
Projectile motion - Why does horizontal velocity remain constant?
horizontal acceleration - gcos90 = 0
Projectile motion - How to calculate magnitude of actual velocity from Vx and Vy?
vertical and horizontal components - Pythagoras!
Actual velocity V=√Vx^2+Vy^2
Projectile motion - How to calculate angle θ made by the velocity?
Velocity to the horizontal:
θ=tan^-1(Vy/Vx)
Describe why the distance travelled by a ball A when thrown at a 30° angle with respect to the horizontal can be equal to the distance travelled by ball B thrown at the same velocity and angle of 60°, without involving any calculations.
Ball A has higher horizontal component of velocity than B. Ball A has lower vertical component of velocity than B.
Vertical component affects the time of flight. Ball A has higher horizontal velocity, but lower time of flight than B. Ball B has lower horizontal velocity, but longer time of flight than A.
It can lead to the range of a ball A thrown at an angle of 30° to the horizontal can be the same as the range of ball B thrown at the same speed at an angle of 60° to the horizontal.
