Avehicle accelerates from 0 to 30 m/s in 10 seconds on a straight road, then travels 15 seconds at a constant velocity.
Next it slows down, coming to a stop in 5 seconds. The car
waits 10 seconds, and then backs up for 5 seconds
accelerating from 0 to -10 m/s. Draw a graph showing the
vehicle's velocity vs time by following these steps.
What is the velocity of the vehicle at 0 seconds?
v m/s

The velocity of the vehicle at 0 s is 0 m/s

Explanation:

The Velocity vs. Time graph of this situation is shown in the attached image. As we can see, we have five segments:

1) When the vehicle accelerates from 0 to 30 m/s in 10 seconds, which means at 0 seconds the vehicle's velocity was 0 m/s. In addition, as the vehicle goes from zero to a positive velocity, we have a positive slope.

2) Then the vehicle travels for 15 seconds at a constant velocity, that is why we do not have a slope in this section, since the vehicle kept its 30 m/s.

3) The vehicle comes to a stop in the next 5 seconds, that is why we observe an abrupt change in the graph and a negative slope.

4) The car  waits 10 seconds in that stop, again we have a line with no slope

5) Finally, the car accelerates from 0 to -10 m/s in the next 5 seconds. This means the car changed its direction.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

80

step-by-step explanation: