topic 3: motion and forces

displacement

change in position of the object

speed

rate of change of distance

velocity

rate of change of displacement

acceleration

rate of change of velocity

kinematics equation + conditions

v = u+at

v² = u²+2as

s = ut + ½ at²

s = ½ (u+v)t

applicable for uniform acceleration in a straight line

v-t graph of throwing a ball upwards (without air resistance)

v-t graph of throwing a ball upwards (without air resistance) + explanation

with air resistance, there will be loss of kinetic energy, so the ball returns to the initial position with a final speed less than initial speed. this means that the average speed upwards is greater than the average speed downwards. since the distance is the same, the time taken to travel up to the maximum height is shorter than the time taken for the ball to travel back down to the initial position.

a-t graph of throwing a ball upwards (with and without air resistance)

v-t graph of ball released from height H above ground (with + without energy loss)

s-t graph of ball released from height H above ground (with + without energy loss)

a-t graph of ball released from height H above ground (with + without energy loss)

newton’s first law

a body at rest will stay at rest, and a body in motion will continue to move at constant velocity, unless acted upon by a resultant external force

newton’s second law

the rate of change of momentum of a body is directly proportional to the resultant force acting on the body and is in the same direction as the resultant force

newton’s third law

the force exerted by one body on a second body is equal in magnitude but opposite in direction to the force simultaneously exerted by the second body on the first body

inertia

the property of a body that resists change in motion

momentum

p = mv

impulse

F Δt = mv - mu = change in momentum = area under F-t graph

resultant force

F = dp/dt

F_net = ma , for constant mass

force if mass of the system is varying (rocket, conveyer belt and helicopter)

rocket: F = v dm/dt (v is the velocity of the air wrt rocket)

conveyer belt: F = v dm/dt

helicopter: F = v² p A (p = density of air, A = area swept out by rotor blades)