A truck with a mass of 20t has a tractive resistance of 280N/t if the truck travels at a speed 72km/h. Calculate the following. a) The distance 36s. b) The power required for the speed.
same as you do with ordinary numeric fractions. Find a common denominator and use that to combine them.
(x-2)/(x+3) + (2x-7)/(x-5) - 3/(x-2)
Common denominator is (x+3)(x-5)(x-2). So, now you can multiply each term by the needed factors:
(x-2)(x-5)(x-2) + (2x-7)(x+3)(x-2) - 3(x+3)(x-5)
------------------------------------------------------------------------------
(x+3)(x-5)(x-2)
(x-2)(x-5)(x-2) (2x-7)(x+3)(x-2) 3(x+3)(x-5)
-------------------- + ------------------- - -------------------------
(x+3)(x-5)(x-2) (x+3)(x-5)(x-2) (x+3)(x-5)(x-2)
(x-2)(x-5)(x-2) (2x-7)(x+3)(x-2) 3(x+3)(x-5)
-------------------- + ------------------- - -------------------------
(x+3)(x-5)(x-2) (x+3)(x-5)(x-2) (x+3)(x-5)(x-2)
(x-2)(x-5)(x-2) + (2x-7)(x+3)(x-2) - 3(x+3)(x-5)
------------------------------------------------------------------------------
(x+3)(x-5)(x-2)
(x-2)(x-5)(x-2) + (2x-7)(x+3)(x-2) - 3(x+3)(x-5)
-------------------------------------------------------------
(x+3)(x-5)(x-2)
To calculate the distance traveled by the truck in 36 seconds, we need to use the formula:
Distance = (Initial Speed × Time) + (0.5 × Accelaration × Time²)
Since the truck is already at a constant speed, the acceleration would be zero. Therefore, the formula becomes:
Distance = Initial Speed × Time
First, we need to convert the speed of the truck from km/h to m/s:
72 km/h = 72,000 m/3600 s = 20 m/s
Now we can calculate the distance:
Distance = 20 m/s × 36 s = 720 meters
So the distance traveled by the truck in 36 seconds is 720 meters.
To calculate the power required for the speed, we can use the equation:
Power = Force × Velocity
First, we need to calculate the force exerted by the tractive resistance:
Force = Tractive Resistance × Mass
In this case, the mass of the truck is given as 20 tons, which can be converted to kilograms:
20 tons = 20,000 kg
Now we can calculate the force:
Force = 280 N/t × 20,000 kg = 5,600,000 N
Finally, we can calculate the power:
Power = Force × Velocity = 5,600,000 N × 20 m/s = 112,000,000 Watt
So the power required for the speed of the truck is 112,000,000 Watts.