Question

A net force of 15 N is applied to a cart with a mass of 2.1 kg. a. What is the acceleration of the cart? b. How long will it take the cart to travel 2.8 m, starting from rest?

Answer 1

The acceleration of the cart is 7.14
`m/s^2`. It will take approximately 0.83 seconds for the cart to travel 2.8 meters, starting from rest.

Step-by-step explanation:

To find the acceleration of the cart, you can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass. In this case, the net force is 15 N and the mass is 2.1 kg, so the acceleration can be calculated as:

acceleration = net force / mass = 15 N / 2.1 kg = 7.14
`m/s^2`

To calculate the time it will take for the cart to travel 2.8 m, starting from rest, you can use the equation of motion:

`distance = (initial velocity * time) + (0.5 * acceleration * time^2)`

Since the cart starts from rest, the initial velocity is 0, so the equation simplifies to:

`distance = 0.5 * acceleration * time^2`

Plugging in the values, we get:

`2.8 m = 0.5 * 7.14 m/s^2 * time^2`

Rearranging the equation and solving for time, we get:

time =
`√((2 * distance) / acceleration)` =
`√(2 * 2.8 m / 7.14 )`
`m/s^2` ≈ 0.83 s