Question

A 1200-kg car pushes a 2100-kg truck that has a dead battery to the right. When the driver steps on the accelerator, the drive wheels of the car push against the ground with a force of 4500 N. Which, if any, of the following gives a correct acceleration constraint for this problem? The variable ac is the acceleration of the car, and the variable t is the acceleration of the truck.

a. ac=at
b. ac=−at
c. ac=21001200at
d. ac=12002100at
e. There are no acceleration constraints for this problem.

Answer 1

Option A: a_c = a_t

Step-by-step explanation:

Let's denote the force acting on the car due to the truck as F_ct

Similarly, the force acting on the truck due to the car is denoted as F_tc.

Now, F_ct = m_c × a_c

Where;

m_c is mass of car

a_c is acceleration of car

Also, F_tc = m_t × a_t

Where;

m_c is mass of truck

a_c is acceleration of truck

Now, since the car is the one pushing the truck, from Newton's laws, we can say that they stick together and move in the same direction at the same acceleration.

Thus, the truck will move with an acceleration equal to that of the car pushing it.

Thus; a_c = a_t