Question: A car is initially at rest at position x = 0 m. After 5 seconds, it starts accelerating uniformly at a rate of 2 m/s^2 for a duration of 10 seconds. Calculate the displacement of the car during this time period.

Answer: To calculate the displacement of the car during this time period, we need to first find the final velocity of the car, and then use the kinematic equation to determine the displacement.

Given: Initial velocity (u) = 0 m/s Acceleration (a) = 2 m/s^2 Time duration (t) = 10 seconds

Step 1: Calculate the final velocity (v): Using the kinematic equation v = u + at, we substitute the given values: v = 0 m/s + (2 m/s^2)(10 s) v = 20 m/s

Step 2: Calculate the displacement (s): Using the kinematic equation s = ut + 0.5at^2, we substitute the given values: s = (0 m/s)(10 s) + 0.5 (2 m/s^2)(10 s)^2 s = 0 + 0.5 (2 m/s^2)(100 s^2) s = 0 + 100 m s = 100 m

Therefore, the displacement of the car during this time period is 100 meters (m).

Note: The positive sign of the displacement indicates that the car moved in the positive x-direction (towards the positive axis), starting from the initial position.