AH 1.1 Kinematic Relationships Flashcards
The linear equations of motion - their derivations and applications.
Derive the kinematic relationship v=u+at
Derive the kinematic relationship
s = ut + 1/2 at2
Derive the kinematic relationship v2 = u2 + 2as
A body undergoes uniform acceleration.
Write down the general equation for its displacement s with respect to time t.
s = ut + ½ at2
The initial velocity of a body is 20 ms-1 and it’s acceleration is 6 ms-2.
Write down the particular equation for the displacement of this body.
s = 20t + 3t2
A body has diplacement equation s = 20t + 3t2
Using differentiation, find the equation for the velocity of this body.
Show all reasoning.
v = ds/dt
= d/dt (20t + 3t2)
v = 20 + 6t
Given the velocity equation for a moving body is v = 20 + 6t, differentiate this velocity equation to confirm that the acceleration is 6 ms-2. Show all steps of reasoning.
a = dv/dt
= d/dt (20 + 6t)
a = 6 ms-2
The displacement of a firework rocket for the first 3 seconds of its motion is given by the equation
s = 8t3 + 4t2
Find expressions for the velocity and acceleration of the rocket. Show all steps of reasoning.
v = ds/dt
v = 24t2 + 8t
a = dv/dt
a = 48t +8
The displacement of a firework rocket is given by s = 8t3 +4t2
After 3 seconds find the displacement of the rocket.
s = 252 m
The velocity of a firework rocket is given by
v = 24t2 + 8t
Find the velocity after 3 seconds.
v = 240 ms-1
The acceleration of a firework rocket is given by the equation a = 48t +8
Findf the acceleration after 3 seconds.
a = 152 ms-2
Give a physical reason for why the displacement, velocity and acceleration equations for a firework rocket after launch only hold for the first 3 seconds.
The firework rocket must have run out of fuel after 3 seconds.
The displacement of a firework rocket after launch is given by s = 8t3 +4t2
Give a mathematical reason why this equation only holds for 3 seconds.
The displacement equation suggests that s increases indefinitely!
This is clearly impossible as there is only a finite amount of fuel.