Question

You're riding a unicorn at 25 m/s and come to a uniform stop at a red light 20m away. What's your acceleration?

Answer 1

The answer is -15.625m/s².

Acceleration is the change in velocity over a period of time. It can be computed using the formula:

$a = \dfrac{vf-vi}{t}$

Where:

vf = final velocity

vi = initial velocity

t = time

Now let's see what was given in your problem:

The car was moving at 25m/s and then came to a stop. So initially it was moving and then it stopped. This means the final velocity will be 0m/s because it stopped moving.

But look at the problem, it shows no time. We need to solve for time from the time it moved till it reached the red light 20 m away.

Time can be computed using the kinematics formula:

$d = \dfrac{vi+vf}{2} *t$

We just derive the formula from the equation by filling out what we know first. 

$20m = \dfrac{25m/s+0m/s}{2}(t)$

$20m = 12.5m/s{2}(t)$

$\dfrac{20m}{12.5m/s}=t$
$1.6s=t$

The time it took from the point it was moving till it stopped is 1.6s. We can now use this in our acceleration formula.

$a = \dfrac{0m/s-25m/s}{1.6s}$

$a = \dfrac{-25m/s}{1.6s}$

$a = -15.625m/s^{2}$

Notice that the acceleration is negative. This means that the car decelerated or slowed down.

Answer 2

Answer:

My acceleration is 15.63 m/s² (slowing down)

Explanation:

The expression for the acceleration is equal:

$v^{2} _{f} -v^{2} _{i} =2ax$

Where

vi = initial speed = 25 m/s

vf = final speed = 0

x = displacement = 20 m

Replacing and clearing the acceleration "a":

$a=\frac{v^{2} _{f} -v^{2} _{i} }{2x} =\frac{0-25^{2} }{2*20} =--15.63m/s^{2}$

The negative sign of acceleration means that it is slowing down