Question

A force acts on a car of mass m so that the speed v of the car increases with position x as v = kx², where k is constant and all quantities are in SI units. Find the force acting on the car as a function of position.

a)F=2mkx
b)F=4mkx
c) F=6mkx
d) F=8mkx

Answer 1

The force acting on the car as a function of position is given by F = 2mkx.

Step-by-step explanation:

The question asks about the force acting on a car as a function of position when the car's speed increases with position according to the equation v = kx². To find the force, we need to differentiate the equation v = kx² with respect to position x to get the equation for acceleration a. The force acting on the car is then given by the equation F = ma, where m is the mass of the car. Since acceleration a is the second derivative of position x, we need to differentiate the equation v = kx² twice to find the force as a function of position.

First derivative of v with respect to x: dv/dx = 2kx

Second derivative of v with respect to x: d²v/dx² = 2k

Since F = ma, the force acting on the car is given by F = 2km

Therefore, the correct option is F = 2mkx.