1. B R Sitaram, Zeal Educational Services Pvt. Ltd.
Which equation to use?
B R Sitaram,
Zeal Educational Services Pvt. Ltd.

2. 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?

3. Which Equation to use? First list the variables that we use: t: time
s: distance
u: initial speed
v: final speed
a: acceleration
Two more variables that can be removed easily:
s0: initial position and t0: initial time.
Which Equation to use?

4. Write the equations: 1. s = u t + 1/2at2 2. v = u + a t 3
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?

5. t s u v a
v = u + at Y N
s = ut+1/2at2
v2 – u2 = 2as
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?

6. Which Equation to use? t s u v a v = u + a t Y N s = u t + ½ a t2
v2 – u2 = 2 a s
s = v t - ½ a t2
s = t (u + v)/2
Which Equation to use?

7. 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?

8. 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?

9. 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?

10. 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?

11. 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?

12. Which Equation to use? Example:
A plane has a takeoff speed of 88.3 m/s and requires 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?