You are driving your car, and the traffic light ahead turns red. You apply the brakes for 2.13 s, and the velocity of the car decreases to +4.90 m/s. The car's deceleration has a magnitude of 3.55 m/s2 during this time. What is the car's displacement?

if the initial velocity was v,

v - 3.55*2.13 = 4.90
v = 12.46 m/s

the displacement s is thus

s = 12.46*2.13 - 3.55/2 * 2.13^2
s = 18.49 m

To find the car's displacement, we need to use the equations of motion. In this case, we can use the equation of motion in one dimension:

v^2 = u^2 + 2as

Where:
v = final velocity (4.90 m/s)
u = initial velocity (unknown)
a = acceleration (deceleration in this case, which is -3.55 m/s^2)
s = displacement (unknown)

Since the initial velocity before applying the brakes is unknown, our goal is to solve for displacement (s).

Rearranging the equation, we have:

s = (v^2 - u^2) / (2a)

Now, let's substitute the known values into the equation:

s = (4.90^2 - u^2) / (2 * -3.55)

Simplifying further:

s = (24.01 - u^2) / -7.10

We still need to find the initial velocity (u) to proceed. For that, we can use another equation of motion:

v = u + at

Rearranging the equation, we have:

u = v - at

Substituting the known values:

u = 4.90 - (-3.55 * 2.13)

Simplifying further:

u = 4.90 + 7.57

u = 12.47 m/s

Now that we have the initial velocity (u), we can substitute it back into the equation for displacement:

s = (4.90^2 - 12.47^2) / (2 * -3.55)

Simplifying further:

s = (24.01 - 155.00) / -7.10

s = (-130.99) / -7.10

s = 18.45 m

Therefore, the car's displacement during the deceleration is 18.45 m.