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?
m/s

The velocity of the vechicle 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.

Explanation:

1) First of all, we need to calculate the heat needed to raise the temperature of the block of lead from the initial temperature (25.0 C) to the melting temperature (327.5 C). This heat is given by the equation

where

m = 2.00 kg is the mass of the block

Cpb = 130.0 J/kg*C is the specific heat capacity of lead

is the temperature difference

Substituting,

2) Now we have to calculate the amount of heat needed to completely melt the lead, which is given by:

where

Hj = 2.04x10^4 J/kg is the latent heat of fusion of lead

Substituting,

3) Therefore, the total heat needed is