In two-dimensional kinematics, we are concerned with the motion of objects in a plane. This can be difficult to visualize, so let’s consider a simple example.
A car is driving down a straight road at a constant speed. The driver then applies the brakes and the car comes to a stop. We can describe this scenario using kinematic equations.
The first equation we will need is the equation for uniform acceleration:
a = (v_f – v_i)/t
Where a is the acceleration, v_f is the final velocity, v_i is the initial velocity, and t is the time interval over which the acceleration occurs.
In our example, we know that the car starts from rest (v_i = 0), so we can simplify this equation to:
a = -v/t
Where v is the car’s velocity at the time when the brakes are applied. We also know that the car comes to a stop (v_f = 0), so we can solve for t:
t = -v/a
Now that we know the value of t, we can plug it back into our original equation to find the acceleration:
a = (0 – 0)/(-v/a)
a = v^2/(-v)
a = -v
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