Question

A man does 4,918 j of work in the process of pushing his 5.3 103 kg truck from rest to a speed of v, over a distance of 33 m. Neglecting friction between the truck and road, determine the final velocity (in m/s) of the truck.

Answer 1

Using the work-energy theorem, the final velocity v of the truck is calculated to be 1.36 m/s after 4,918 J of work is applied to push the 5.3 x 10^3 kg truck over a distance of 33 m, starting from rest and neglecting friction.

Step-by-step explanation:

To determine the final velocity (v) of the truck, we can apply the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy (KE). Since the truck is pushed from rest, its initial kinetic energy is zero and the work done will be equal to its final kinetic energy.

The work-energy theorem is given by the equation:
Work = ½ mv^2

Where:
m is the mass of the truck (5.3 × 10^3 kg)
v is the final velocity of the truck
Work is the work done (4,918 J)

Rearranging the formula to solve for v, we get:

v = √(2 × Work/m)
v = √(2 × 4,918 J / (5.3 × 10^3 kg))
v = √(0.001855 × 10^3 m^2/s^2)
v = √1.855 m^2/s^2
v = 1.36 m/s

Thus, the final velocity v of the truck is 1.36 m/s.