Answer:
The magnitude of the acceleration of the car is 35.53 m/s²
Explanation:
Given;
acceleration of the truck, 
= 12.7 m/s²
mass of the truck, 
= 2490 kg
mass of the car, 
= 890 kg
let the acceleration of the car at the moment they collided = 
Apply Newton's third law of motion;
Magnitude of force exerted by the truck = Magnitude of force exerted by the car.
The force exerted by the car occurs in the opposite direction.
Therefore, the magnitude of the acceleration of the car is 35.53 m/s²
The output of the machine is
(output work) = (output force) x (distance)
450 N-m = (output force) x (3 meters)
Divide each side
by 3 meters: Output force = (450 N-m) / (3 m)
= 150 newtons .
With all the information given about the output work, we don't need
to know anything about the input work, or even the fact that we're
dealing with a machine.
It's comforting, though, to look back and notice that the output work
(450 N-m) is not more than the input work (500 N-m). So everything
is nice and hunky-dory.
___________________________________
Well, my goodness !
I didn't even need to go through all of that.
Given:
-- The input force to the machine is 50 newtons.
-- The mechanical advantage of the machine is 3 .
That right there tells us that
-- The output force of the machine is 150 newtons.
We don't need any of the other given information.
We are missing an important piece of information needed to answer this question: the number of kcal Charles losses per day. However, we can come up with a general equation in which kcal/day is the only independent variable.
We know that it takes 3500 kcal to lose one pound. To lose 5 pounds, Charles needs to lose 5 x 3500 kcal = 17,500 kcal.
To find how many days it takes Charles to lose 17,500 kcal (5 pounds), we must divide that amount by the number of kcal Charles loses per day.
Here is the equation to calculate that number
Number of days= 17500 / (kcal per day)
If given calories, remember that 1000 calories = 1 kcal, and .001 kcal = 1 cal
The Young modulus is given by:
where
F is the force applied
is the initial length of the wire
is the cross-sectional area of the wire
is the stretch of the wire
The wire in the problem stretches by
of its length, this means
We can also calculate the area of the wire; its radius is in fact half the diameter:
and so the area is
We know the force applied to the wire, F=20 N, so now we have everything to calculate the Young modulus:
Answer:
(B) (length)/(time³)
Explanation
The equation x = ½ at² + bt³ has to be dimensionally correct. In other words the term bt³ and ½ at² must have units of change of position = length.
We solve in order to find the dimension of b:
[x]=[b]*[t]³
length=[b]*time³
[b]=length/time³
