A 2340 kg car traveling to the west at 20.7

m/s slows down uniformly under a force of
8340 N to the east.
a) How much force would be required to
cause the same acceleration on a car of mass
3180 kg?
Answer in units of N.

b) How far would the car move before stop-
ping?
Answer in units of m.

a=F/m so F and m would have to go up at the same rate to keep the same ration.

F/m=F/m
F/3180=8340/2340
solve for F

To answer part a) of the question, we need to determine the acceleration of the car first. We can find the acceleration by using Newton's second law of motion:

Force = mass * acceleration

Given:
Mass of the first car (m1) = 2340 kg
Force on the first car (F1) = -8340 N (opposite direction of motion)
Velocity of the first car (v1) = -20.7 m/s (opposite direction of the force)

Since the car is slowing down uniformly, we can assume the acceleration is negative and equal to the force divided by the mass:

Acceleration (a1) = F1 / m1

Now, we can calculate the acceleration:

Acceleration (a1) = -8340 N / 2340 kg

To find the force required for a car of mass 3180 kg, we'll use the same acceleration value:

Force (F2) = m2 * a1

Given:
Mass of the second car (m2) = 3180 kg
Acceleration (a1) = -8340 N / 2340 kg

Now, we can calculate the force required for the second car:

Force (F2) = 3180 kg * (-8340 N / 2340 kg)

To solve this equation, we can cancel out the units (kg) and calculate the force:

Force (F2) = 3180 * (-8340 / 2340) N

The answer in part a) is the calculated value of force (F2) in units of Newtons.

Next, to answer part b) of the question, we need to find the distance traveled by the car before stopping. We can use the equation of motion:

v^2 = u^2 + 2as

Where:
v = final velocity (0 m/s, since the car comes to a stop)
u = initial velocity (-20.7 m/s)
a = acceleration (calculated in part a)
s = distance traveled (what we need to find)

We rearrange the equation to solve for distance (s):

s = (v^2 - u^2) / (2a)

Given:
Final velocity (v) = 0 m/s
Initial velocity (u) = -20.7 m/s
Acceleration (calculated in part a) = a1

Now, we can calculate the distance traveled before stopping:

s = (0^2 - (-20.7)^2) / (2 * a1)

Plug in the values and solve the equation to find the distance (s), which will be in units of meters.

Note: Make sure to substitute the value of acceleration (a1) calculated in part a) into the equation to get an accurate answer.