Question

A toy car with a mass of 5.5 kg is moving horizontally over flat ground at a speed of 2.1 m/s. An unknown force then directly pushes the car for a distance of 3 meters, after which the car has a speed of 7.3 m/s. You may assume that air resistance and friction are both negligible. What was the magnitude of the unknown force

Answer 1

The magnitude of the unknown force is 44.8 N.

Step-by-step explanation:

The force can be found with Newton's second law:

`F = ma`

Where:

m: is the mass of the toy car = 5.5 kg

a: is the acceleration

F: is the force =?

We can calculate the acceleration with the following kinematic equation:

`v_(f)^(2) = v_(0)^(2) + 2ad`

Where:

`v_(f)`: is the final speed = 7.3 m/s

`v_(0)`: is the initial speed = 2.1 m/s

d: is the distance traveled = 3 m

Hence, the acceleration is:

`a = (v_(f)^(2) - v_(0)^(2))/(2d) = ((7.3 m/s)^(2) - (2.1 m/s)^(2))/(2*3 m) = 8.15 m/s^(2)`

Finally, the magnitude of the force is:

`F = ma = 5.5 kg*8.15 m/s^(2) = 44.8 N`

Therefore, the magnitude of the unknown force is 44.8 N.

I hope it helps you!