Question:

A car starts from rest and accelerates uniformly at $2 \, \text{m/s}^2$ for a total of 10 seconds. After this initial acceleration period, the car continues to travel at a constant velocity for an additional 20 seconds.

a) What is the displacement of the car during the initial 10 seconds of acceleration? b) What is the displacement of the car during the next 20 seconds of constant velocity motion? c) What is the total displacement of the car during the 30 seconds?

Answer:

a) To find the displacement of the car during the initial 10 seconds of acceleration, we can use the kinematic equation:

Here, the initial velocity $v_i$ is 0 m/s, the acceleration $a$ is $2 \, \text{m/s}^2$, and the time $t$ is 10 seconds. Plugging in these values into the equation, we get:

Simplifying the equation gives us:

Therefore, the displacement of the car during the initial 10 seconds of acceleration is 100 meters.

b) During the next 20 seconds of constant velocity motion, the car travels at a constant speed, which means its velocity remains unchanged. Since the velocity remains constant, the displacement can be found using the equation:

Here, the velocity $v$ is the same as the velocity at the end of the acceleration period, which is $2 \, \text{m/s}^2$. The time $t$ is 20 seconds. Plugging in these values into the equation gives:

Therefore, the displacement of the car during the next 20 seconds of constant velocity motion is 40 meters.

c) To find the total displacement of the car during the 30 seconds, we add the displacements from parts a) and b).

Therefore, the total displacement of the car during the 30 seconds is 140 meters.