A small car of mass 985 kg is parked behind a small truck of mass 1551 kg on a level road. The brakes of both the car and the truck are off so that they are free to roll with negligible

friction. A 83 kg woman sitting on the tailgate of the truck shoves the car away by exerting a constant force on the car with her feet. The car accelerates at 0.3 m/s2. What is the acceleration of the truck?
Answer in units of m/s2

The mass of the car, m = 985 kg, acceleration of the car, a = 0.3 m/s^2

According to Newton's 2nd law, force exerted on the car,
F = ma = 985 x 0.3 = 295.5 N
According to Newton's 3rd law, the same force in the opposite direction will be exerted on the truck.

Mass of the truck with the woman, M = 1551 + 83 = 1634 kg
Force acting on the truck, F = 1634 N [ same as the force on the car ]
F = M•a1 or, a1 = F/M = 295.5/1634 = 0.18 m/s^2
So the acceleration of the truck will be 0.18 m/s^2 and it's direction will be opposite of the car's acceleration.

Well, it seems like the woman on the tailgate of the truck just couldn't resist giving the car a good shove! Let's see what happens.

Now, the car has a mass of 985 kg and accelerates at 0.3 m/s². Since we're looking for the acceleration of the truck, let's call it "a_t."

According to Newton's second law, the net force acting on an object is equal to its mass multiplied by its acceleration. So for the car, we have:

Force_car = mass_car * acceleration_car

Now, the woman on the tailgate only pushes the car, so the force exerted by the woman is what accelerates the car:

Force_car = force_woman

Similarly, for the truck:

Force_truck = mass_truck * acceleration_truck

However, since there are no external forces acting on the truck other than the force exerted by the woman, we can say that:

Force_truck = force_woman

If we set these two equations equal to each other, we get:

mass_car * acceleration_car = mass_truck * acceleration_truck

Now, we can plug in the given values to solve for the acceleration of the truck:

985 kg * 0.3 m/s² = 1551 kg * acceleration_truck

acceleration_truck = (985 kg * 0.3 m/s²)/(1551 kg)

After simplifying, the acceleration of the truck is approximately 0.189 m/s². So, let's hope that the woman on the tailgate doesn't find herself on a truck that accelerates too quickly!

To find the acceleration of the truck, we can start by calculating the net force acting on the car.

The force exerted by the woman on the car is given as the mass of the woman (83 kg) multiplied by the acceleration of the car (0.3 m/s^2). We can calculate this as:

Force on car = mass of woman * acceleration of car
Force on car = 83 kg * 0.3 m/s^2
Force on car = 24.9 N

Since the car and the truck are connected and there is no friction, the force on the car is equal to the force on the truck. So, the force on the truck is also 24.9 N.

To find the acceleration of the truck, we can use Newton's second law of motion:

Force on truck = mass of truck * acceleration of truck

Rearranging the equation, we get:

acceleration of truck = Force on truck / mass of truck

Plugging in the values, we have:

acceleration of truck = 24.9 N / 1551 kg
acceleration of truck ≈ 0.0161 m/s^2

Therefore, the acceleration of the truck is approximately 0.0161 m/s^2.

To find the acceleration of the truck, we can start by analyzing the forces acting on the system.

1. Weight (mg): The weight of the objects acts vertically downwards. The weight force on the car is given by:
Fc = mc * g, where mc is the mass of the car and g is the acceleration due to gravity (usually taken as 9.8 m/s^2). Similarly, the weight force on the truck is given by: Ft = mt * g, where mt is the mass of the truck.

2. Force exerted by the woman: The woman is exerting a constant force on the car, causing it to accelerate. Let's call this force F applied by the woman.

3. Force of inertia: As the car accelerates, an equal and opposite force of inertia acts on the woman, according to Newton's third law of motion. We'll call this force Fi exerted on the woman.

Since the car and truck are connected and have negligible friction, they move together as a single system. Therefore, the net horizontal force acting on the entire system should be equal to the mass of the system multiplied by its acceleration.

Net horizontal force on the system = (mc + mt) * a

Now let's consider the individual forces:

For the car:
Force exerted by the woman = F
Weight force = mc * g

So, net horizontal force on the car = F - mc * g

For the truck:
Force exerted by the woman = -F (opposite direction)
Force of inertia on the woman = Fi
Weight force = mt * g

So, net horizontal force on the truck = -F - Fi - mt * g

Since the net horizontal force acting on the entire system is equal to the net horizontal force on the car plus the net horizontal force on the truck:

(mc + mt) * a = (F - mc * g) + (-F - Fi - mt * g)

Simplifying the equation:

(mc + mt) * a = -mc * g - Fi - mt * g

mc * g and mt * g are the weights of the car and truck, respectively. So, let's rewrite the equation:

(mc + mt) * a = -Weight of car - Weight of truck - Fi

Adding mc * g and mt * g to both sides:

(mc + mt) * a + mc * g + mt * g = -Fi

Since Fi is the inertial force experienced by the woman, we know that Fi = mw * a, where mw is the mass of the woman.

Substituting mw * a for Fi:

(mc + mt) * a + mc * g + mt * g = -mw * a

Now, we can solve for a, the acceleration of the truck:

(mc + mt) * a = -mc * g - mt * g - mw * a

Rearranging the equation:

(mc + mw + mt) * a = -mc * g - mt * g

a = (-mc * g - mt * g) / (mc + mw + mt)

Substituting the given values:
mc = 985 kg (mass of the car),
mt = 1551 kg (mass of the truck),
mw = 83 kg (mass of the woman),
g = 9.8 m/s^2 (acceleration due to gravity),

we can calculate the acceleration of the truck using the formula:

a = [-(985 kg * 9.8 m/s^2) - (1551 kg * 9.8 m/s^2)] / (985 kg + 83 kg + 1551 kg)

Calculating the numerator:

-(985 kg * 9.8 m/s^2) - (1551 kg * 9.8 m/s^2) = -17642.4 kg m/s^2

And calculating the denominator:

985 kg + 83 kg + 1551 kg = 2619 kg

Finally, calculating the acceleration:

a = (-17642.4 kg m/s^2) / (2619 kg)

a ≈ -6.73 m/s^2

Therefore, the acceleration of the truck is approximately -6.73 m/s^2. Note that the negative sign indicates that the truck is accelerating in the opposite direction to the car's acceleration.