Equations of motion with constant acceleration
First: Remember that constant acceleration is a change in speed by equal amounts over equal time
intervals.
Example: A stationary car starts moving such that its speed becomes (5𝑚/𝑠) after one second, then its
speed becomes (10𝑚/𝑠) after another second, then its speed becomes (15𝑚/𝑠) after another second, and
so on. We observe that the speed increases every second by a constant amount of (5𝑚/𝑠). We then say
that the car is moving with a constant acceleration of (5𝑚/𝑠 2 ).
Second: Any object moving with constant acceleration can have its motion described using the following
equations:
𝑣𝑓 = 𝑣𝑖 + 𝑎𝛥𝑡
𝑣𝑓2 = 𝑣𝑖2 + 2𝑎𝑑
1
𝑑 = 𝑣𝑖 𝛥𝑡 + 𝑎𝛥𝑡 2
2
Where:
𝑣𝑖 : Initial velocity of the object (i.e., before the change)
𝑣𝑓 : Final velocity of the object (i.e., after the change)
𝑎: Acceleration
𝛥𝑡: Time
𝑑: Displacement
Important Notes:
① The values of the variables must be substituted into the following units:
𝑣: (𝑚/𝑠) 𝑎: (𝑚/𝑠 2 ) 𝛥𝑡: (𝑠) 𝑑: (𝑚)
② The values of the variables must be replaced with North
(+)
the appropriate signs according to the direction.
West East
(-) (+)
③ If the object moves from rest → (𝑣𝑖 = 0)
If the object stops → (𝑣𝑓 = 0)
South
(-)
First: Remember that constant acceleration is a change in speed by equal amounts over equal time
intervals.
Example: A stationary car starts moving such that its speed becomes (5𝑚/𝑠) after one second, then its
speed becomes (10𝑚/𝑠) after another second, then its speed becomes (15𝑚/𝑠) after another second, and
so on. We observe that the speed increases every second by a constant amount of (5𝑚/𝑠). We then say
that the car is moving with a constant acceleration of (5𝑚/𝑠 2 ).
Second: Any object moving with constant acceleration can have its motion described using the following
equations:
𝑣𝑓 = 𝑣𝑖 + 𝑎𝛥𝑡
𝑣𝑓2 = 𝑣𝑖2 + 2𝑎𝑑
1
𝑑 = 𝑣𝑖 𝛥𝑡 + 𝑎𝛥𝑡 2
2
Where:
𝑣𝑖 : Initial velocity of the object (i.e., before the change)
𝑣𝑓 : Final velocity of the object (i.e., after the change)
𝑎: Acceleration
𝛥𝑡: Time
𝑑: Displacement
Important Notes:
① The values of the variables must be substituted into the following units:
𝑣: (𝑚/𝑠) 𝑎: (𝑚/𝑠 2 ) 𝛥𝑡: (𝑠) 𝑑: (𝑚)
② The values of the variables must be replaced with North
(+)
the appropriate signs according to the direction.
West East
(-) (+)
③ If the object moves from rest → (𝑣𝑖 = 0)
If the object stops → (𝑣𝑓 = 0)
South
(-)
