This type of motion is defined as the motion of an object in which the object travels in a straight line and its velocity remains constant along that line as it covers equal distances in equal intervals of time, irrespective of the duration of the time.
When an object is travelling in a straight line with an increase in velocity at equal intervals of time, then the object is said to be in uniform acceleration. Free falling of an object is an example of uniform acceleration.
There are 4 equations which can be used whenever an object travels with constant, uniform acceleration in a straight line.
Suppose an object is travelling at a velocity u and then moves with a uniform accelerationa for a time t. Its velocity is then v and it has travelled a distance s.
Image: Harrage, E. (2023). Equations of motion (CC BY)
You can remember the 5 symbols by "suvat". If you know any three of suvat, the other two can be found.
In questions, initially at rest means u = 0. A negative number for the acceleration means the object is decelerating (slowing down).
Example:
A cheetah starts from rest and accelerates at 2 m/s2 for 10 seconds. Calculate:
a) the final velocity
b) the distance travelled.
First write out suvat:
s = ?
u = 0
v = ?
a = 2 m/s2
t = 10 s
a) Use equation 1: v = u + at
v = 0 + 2 x 10
v = 20 m/s
b) Use equation 2:
Example:
A nail is fired from a nail gun into a fixed block of wood. The nail has a speed of 380 m/s just as it enters the wood. The nail comes to rest after penetrating 60 mm into the wood. Find the time taken for the nail to come to rest. Assume that the retarding force on the nail is constant as it penetrates the wood.
S = 60 mm or 60 × 10-3 cm
u = 380 m/s
v = 0
a = ?
t = ?
Use the equation: v2 = u2 + 2as
02 = 3802 + 2a × 60 × 10-3
a = -1,203,333 ms-2
v = u +at
0 = 380 + (-1,203,333)t
t = 0.0003157 seconds
The time taken for the nail to come to rest is 3.16 × 10-4 s.
Myhometuition. (2014). Equations of uniform acceleration (Standard YouTube licence)