Kinematics in Two Dimensions
Displacement: r  r  r0
Average velocity: vave 
r r  r0

t t  t 0
Average acceleration: aave 
v v  v0

t
t  t0
r
t  0  t
Instantaneous velocity: v  lim
v
t  0  t
Instantaneous acceleration: a  lim
Note: In two dimensional motion, each component (x and y) can be treated separately.
The x-component is independent of the y-component and vice versa. The two components are
connected by time t.
Equations of Constant Acceleration:
x-component of motion
y-component of motion
v x  v0 x  a x t
v y  v0 y  a y t
1
( v0 x  v x ) t
2
1
x  x0  v0 x t  a x t 2
2
2
2
v x  v0 x  2a x ( x  x0 )
1
( v0 y  v y )t
2
1
y  y0  v0 y t  a y t 2
2
2
2
v y  v0 y  2a y ( y  y0 )
x  x0 
y  y0 
Projectile Motion:
 In projectile motion, we assume no air resistance so:
ax = 0 m/s2
ay = -9.8 m/s2 (assuming up is +)
 Since ax = 0 m/s2, the 4 equations for the horizontal component of projectile motion reduce
down to two:
v x  v0 x
x  x0  v0 xt
 The equations for the vertical component of projectile motion are the same as the
above equations for the y-component of motion with ay = -9.8 m/s2