Answer:
Explanation:
Given
car A had a head start of 
and it starts at x=0 and t=0
Car B has to travel a distance of 
where
is the distance travel by car A in time t
distance travel by car A is

For car B with speed 



Since momentum is a vector quantity, take any direction as positive and other as negative. Answer won't change.
Answer:
the theoretical maximum energy in kWh that can be recovered during this interval is 0.136 kWh
Explanation:
Given that;
weight of vehicle = 4000 lbs
we know that 1 kg = 2.20462
so
m = 4000 / 2.20462 = 1814.37 kg
Initial velocity
= 60 mph = 26.8224 m/s
Final velocity
= 30 mph = 13.4112 m/s
now we determine change in kinetic energy
Δk =
m(
² -
² )
we substitute
Δk =
×1814.37( (26.8224)² - (13.4112)² )
Δk =
× 1814.37 × 539.5808
Δk = 489500 Joules
we know that; 1 kilowatt hour = 3.6 × 10⁶ Joule
so
Δk = 489500 / 3.6 × 10⁶
Δk = 0.13597 ≈ 0.136 kWh
Therefore, the theoretical maximum energy in kWh that can be recovered during this interval is 0.136 kWh
Answer:

Explanation:
The heaviside function is defined as:

so we see that the Heaviside function "switches on" when
, and remains switched on when 
If we want our heaviside function to switch on when
, we need the argument to the heaviside function to be 0 when 
Thus we define a function f:

The
term inside the heaviside function makes sure to displace the function 5 units to the right.
Now we just need to add a scale up factor of 240 V, because thats the voltage applied after the heaviside function switches on. (
when
, so it becomes just a 1, which we can safely ignore.)
Therefore our final result is:

I have made a sketch for you, and added it as attachment.