Tips for solving kinematics exercises

1. Use the speed time function!

v = v ₀ + at

Caption:
v = final velocity
v ₀ = initial velocity
a = acceleration
t = instant of time

Use this function when :

• You know the value of the initial velocity ( v ₀ ), the acceleration ( a ) and the time ( t ) and you want to calculate the final velocity ( v );
• You know the value of the initial velocity ( v ₀ ), the acceleration ( a ), the final velocity ( v ) and you want to calculate the time ( t );
• You know the value of the initial velocity ( v ₀ ), the final velocity ( v ), the time ( t ), but you want to calculate the acceleration ( a );
• You know the value of the final velocity ( v ), the acceleration ( a ) and the time ( t ), but you want to calculate the value of the initial velocity ( v ₀ ).

Note: With this equation, it is not possible to calculate the displacement ( ΔS ).

Solve some exercises: Exercises on average acceleration

2. Use Torricelli’s equation!

v² = v ₀ ²+ 2.a.ΔS

Legend:
v = final velocity
v ₀ = initial velocity
a = acceleration
ΔS = displacement

Use this function when:

• You know the value of the initial velocity ( v ₀ ), the final velocity ( v ), the acceleration ( a ) and you want to calculate the displacement ( ΔS );
• You know the value of the initial velocity ( v ₀ ), the final velocity ( v ), the displacement ( ΔS ) and you want to calculate the acceleration ( a );
• You know the value of the initial velocity ( v ₀ ), of the acceleration ( a ), of the displacement ( ΔS ) and you want to calculate the value of the final velocity ( v );
• You know the value of the final velocity, the acceleration ( a ), the displacement ( ΔS ) and you want to calculate the value of the initial velocity ( v ₀ ).

Note: With this equation, it is not possible to calculate the time ( t ).

Solve some exercises: Exercises on Torricelli’s equation

3. Use the average velocity equation!

ΔS = (v + v ₀ ).t
        2

Caption:
v = final velocity
v ₀ = initial velocity
a = acceleration
ΔS = displacement
t = instant of time

Use this function when:

• You know the value of the displacement ( ΔS ), the initial velocity ( v ₀ ), the final velocity ( v ), but you do not know the instant of time ( t );
• You know the value of the displacement ( ΔS ), the initial velocity ( v ₀ ), the instant of time ( t ), but you do not know the final velocity ( v );
• You know the value of the displacement ( ΔS ), the final velocity ( v ), the instant of time ( t ), but you do not know the value of the initial velocity ( v ₀ );
• You know the value of the final velocity ( v ), the initial velocity ( v ₀ ), the instant of time ( t ), but you do not know the displacement ( ΔS ).

Note: With this equation, it is not possible to calculate the acceleration ( a ).

4. Use position time function!

ΔS = v ₀ .t + a.t² ​​​​2
                   

Caption:
v ₀ = initial velocity
a = acceleration
ΔS = displacement
t = instant of time

Use this function when:

• You know the value of the displacement ( ΔS ), the initial velocity ( v ₀ ), the acceleration ( a ), but you do not know the instant of time ( t );
• You know the value of displacement ( ΔS ), initial velocity ( v ₀ ), time ( t ), but you don’t know the value of acceleration ( a );
• You know the value of the displacement ( ΔS ), the acceleration, the time ( t ), but you don’t know the value of the initial velocity ( v ₀ );
• If you know the value of the acceleration ( a ), the time ( t ), the initial velocity ( v ₀ ), but you don’t know the value of the displacement ( ΔS ).

Note : With this equation, it is not possible to calculate the final velocity ( v ).

If you’re doing some exercise and you notice that two variables are missing, you can use two of the formulas above, figuring out each of those variables in turn. For each formula above, it is assumed that only one variable is missing, which will be its unknown. To solve the equation, you must always isolate it.