Motion in Two Dimensions with Constant Acceleration

time

2

initial position
initial velocity
acceleration

A particle starting at position

→

r

0

with initial velocity

→

v

0

subjected to a constant acceleration

→

a

follows a trajectory given by



r

(t)=



v

0

+



v

0

t+

1

2



a

t

2

. For one-dimensional motion, say in the

x

direction, this reduces to

x(t)=x

0

+v

0

t+

1

2

at

2

. A projectile fired upward at an angle describes a parabolic trajectory when subject to the downward acceleration of gravity. The path of the particle up to the time

t

is shown by a dotted curve.