Application of pseudo force in the given question

Question (17.38, Hibbeler Dynamics SI Edition):

A force of $$P = 300\,\mathrm N$$ is applied to the $$60\:\text{kg}$$ cart. Determine the reactions at both the wheels at A and both the wheels at B. Also, what is the acceleration of the cart? The mass center of the cart is at G.

In the question above, we can clearly see that the force is pulling towards the left, and hence the acceleration of $$4.33\: \text{m/s}^2$$ occurs towards the left. But while solving for the reaction forces at the wheels of the cart, why do we consider the force $$ma$$ acting towards the right? This question is from an exercise that has a lot of questions involving pseudo/d'Alembert forces.

• By including the pseudo-force you are now solving a statics problem. Dec 21, 2019 at 6:03
• @Farcher I understand that, but will the effects of this pseudo force even be felt in real life? What I mean is, say when we are going up in an elevator, we feel 'heavier'. Is the pseudo force used in the question actually going to have an effect like this? Dec 21, 2019 at 9:49
• The pseudo force is very well felt in real life. A great example is when you are in a car taking a turn. You experience a centrifugal force outward while the car is under a centripetal force inwards.
– Sam
Dec 21, 2019 at 10:41