Which equation to use?
B R Sitaram,
Zeal Educational Services Pvt. Ltd.
When students learn the equations of
motion with constant acceleration, they
often get confused: which equation should
we use in a given situation?
This presentation shows a simple way of
deciding!
Which Equation to use?
First list the variables that we use:
1.t: time
2.s: distance
3.u: initial speed
4.v: final speed
5.a: acceleration
Two more variables that can be removed
easily:
s0: initial position and t0: initial time.
Which Equation to use?
Write the equations:
1. s = u t + 1/2at2
2. v = u + a t
3. v2-u2=2 a s
Make a table, showing which are the
variables used in each equation:
Which Equation to use?
t
s
u
v
a
v = u + at
Y
N
Y
Y
Y
s = ut+1/2at2
Y
Y
Y
N
Y
v2 – u2 = 2as
N
Y
Y
Y
Y
Note: Each equation involves four of the five variables!
Two equations appear to be missing: one not involving u
and one not involving a.
They are:
s = vt – 1/2at2
s = t(u+v)/2
Which Equation to use?
t
s
u
v
a
v=u+at
Y
N
Y
Y
Y
s = u t + ½ a t2
Y
Y
Y
N
Y
v2 – u2 = 2 a s
N
Y
Y
Y
Y
s = v t - ½ a t2
Y
Y
N
Y
Y
s = t (u + v)/2
Y
Y
Y
Y
N
Which Equation to use?
In all problems:
 4 variables will be referred to
 3 will be given, 1 to be determined
Use the table and determine which
equation to use
 Solve the equation!

Which Equation to use?
Example:
 I throw a ball up with speed u against
gravity. How much time does it take to reach
the top of its motion?
 Variables: u, a (gravity), v (= 0 at top), t (to be
determined)

Hence use v = u + a t
Which Equation to use?
Example:
 I throw a ball up against gravity. It takes 2
sec to reach the top of its flight. To what
height does it go?
Variables: v (=0 at top), t, a (gravity), s (to be
determined)
 Hence, use s = v t – ½ a t2

Which Equation to use?
Example:
 The Lamborghini Murcielago can accelerate
from 0 to 27.8 m/s (100 km/hr or 62.2 mi/hr)
in a time of 3.40 seconds. Determine the
acceleration of this car in both m/s/s and
mi/hr/s.
Variables: u (=0), v (=27.8 m/s), t (3.40 s), a (to
be determined)
 Hence, use v = u + a t

Which Equation to use?
Example:

A Formula One car is a single-seat racing car with
an open cockpit and substantial wings located in the
front and rear. At high speeds, the aerodynamics of
the car help to create a strong downward force
which allows the car to brake from 27.8 m/s (100
km/hr or 62.2 mi/hr) to 0 in as small of a distance as
17 meters. Determine the deceleration rate (i.e.,
acceleration) achieved by such a car.

Variables: u (=27.8 m/s), v (=0), s (17m), a (to be
determined)
Hence, use v2 – u2 = 2as

Which Equation to use?
Example:

A plane has a takeoff speed of 88.3 m/s and requires
1365 m to reach that speed. Determine the
acceleration of the plane and the time required to
reach this speed.
Variables: u (=0), v (=88.3 m/s), s (=1365 m), a (to be
determined in 1st part), t (to be determined in 2nd part)
 1st part: (u, v, s, a), use v2-u2=2as
 2nd part: (u, v, s, t), use s = t (u + v)/2
 (You can in fact use any equation for part 2, as 4 out of
the 5 variables are now known!)

Which Equation to use?