Question

Shakina and Juliette set the car's initial velocity to zero and set the acceleration to +1.2 m/s2, then clicked "start." Answer the following questions.

What is the car's displacement between 0 and 10.0 s?

What was the total distance traveled by the car during this time interval?

Answer 1

Using the kinematic equation for displacement with constant acceleration, the car's displacement and the total distance traveled between 0 and 10.0 seconds, with an acceleration of +1.2 m/s², is calculated to be 60 meters.

Step-by-step explanation:

To answer the question regarding the car's displacement between 0 and 10.0 s with a constant acceleration of +1.2 m/s2, we can use the kinematic equation for displacement with constant acceleration, which is given by x = x0 + v0t + ½ at2, where x0 is the initial displacement, v0 is the initial velocity, a is the acceleration, and t is the time. With an initial velocity v0 = 0 and initial displacement x0 = 0, the equation simplifies to x = ½ at2. Plugging in the values, we get x = ½ * (1.2 m/s2) * (10.0 s)2 = 60 m, so the car's displacement is 60 meters.

Since the car does not change direction and has a constant acceleration, the total distance traveled is the same as the magnitude of the displacement. Thus, the total distance is also 60 meters.

Answer 2

Let's start by differentiating the terms distance and displacement. They both refer to the length of paths. Distance only accounts for the total length regardless of the path taken. Displacement measures the linear path from the starting point to the end point. So, it does not necessarily follow the actual path. However, for this problem, assuming that the path is just in one direction, displacement and distance would just be equal. The equation would be:

Distance = Displacement = v₀t + 0.5at² = 0(10 s) + 0.5(+1.2 m/s²)(10 s)²
Distance = Displacement = 60 meters