Kinematics | Motion with Constant Acceleration

Question

When a driver hits the brakes, his car decelerates at a uniform rate of 2.0 m/s². His car stops at 9.0 m. How long does it take him to stop?

I have the following variables:

Displacement = 9 meters

t = unknown

v_I = ?

v_F = 0 meters per second

Acceleration = -2.0 meters per second squared

How do I start the problem?

Answer 1

Of the five variables in kinematics (d, t, v₁, v_f, a), we do NOT know v₁ and we are NOT interested in knowing it either. Therefore, we should pick a kinematics equation that excludes v₁ (and hence includes the rest). That equation is:

d = (-1/2) a t² + v_f t

Plugging in the known values into the above equation, takes us to:

9 = (-1/2) * (-2) * t² + 0 * t

--> 9 = t²

--> 3 = t

Therefore, it took the vehicle 3 seconds to stop.

Answer 2

In this case, we need to use one kinematics equation to find the initial velocity and then another to find the time.

First, we'll use

v_f² = v_i² + 2ad

Like you said above, v_f = 0, a = -2 ^m/_s² and d = 9. Plugging these values into the above equation we get

0 = v_i² + 2(-2)(9)

0 = v_i² - 36

36 = v_i²

6 = v_i

Now we know our initial velocity and we can use that to find our time

v_f = v_i + at

0 = 6 -2t

-6 = -2t

3 = t