a car traveling at 30 meters per second begins to slow down at a constant rate. after 2 seconds its velocity is 16 meters per second. write an equation that represents the cars velocity v after t seconds

Let the acceleration (really deceleration) be a

so v = at + c
when t=0 , v = 30
30 = 0 + c, --> c=30
so v = at + 30
when t=2, v = 16
16 = 2a + 30
2a = -14
a = -7

v = -7t + 30

I just solved your question using Calculus, but I am not sure if you know Calculus, so ....

Treat your data two ordered pairs (0,30) and (2,16)
where the first coordinate is time and the second is velocity
slope = (30-16)/(0-2) = -7
so v = -7t + b , using the old y = mx + b format
but (0,30) must satisfy this
30 = 0 + b
b = 30

so v = -7t + 30 , as before

To write an equation representing the car's velocity after t seconds, we need to determine the relationship between velocity and time. We are given that the car's initial velocity is 30 meters per second and after 2 seconds its velocity is 16 meters per second, indicating that the car is slowing down.

We can use the formula for constant acceleration to find the equation:
v = u + at

Where:
v is the final velocity,
u is the initial velocity,
a is the acceleration, and
t is the time.

In this case, the car is slowing down, which means the acceleration is negative. Let's assume the acceleration is a. Since the car is slowing down, the final velocity (v) will be less than the initial velocity (u). So we can rewrite the equation as:

v = u - at

Now, let's plug in the given values:
u = 30 m/s (initial velocity)
v = 16 m/s (velocity after 2 seconds)
t = 2 s (time taken)

Using these values in the equation, we can solve for a:

16 = 30 - 2a

Rearranging the equation:

2a = 30 - 16
2a = 14
a = 7

Now that we have the value of acceleration (a = -7, since it is negative in this case), we can rewrite the equation to represent the car's velocity (v) after t seconds:

v = 30 - 7t

Therefore, the equation that represents the car's velocity (v) after t seconds is v = 30 - 7t.