Identify the initial velocity (u), final velocity (v), and time (t) for the first 4 seconds.

Here's the solution to the problem based on the provided speed-time graph: a) Acceleration in the first 4 seconds. Step 1: Identify the initial velocity (u), final velocity (v), and time (t) for the first 4 seconds. The object starts from rest, so u = 0 m/s. After 4 seconds, the speed is v = 20 m/s. The time taken is t = 4 s. Step 2: Calculate the acceleration using the formula a = (v - u)/(t). a = 20 m/s - 0 m/s4 s a = 20 m/s4 s a = 5 m/s^2 The acceleration in the first 4 seconds is 5 m/s^2. b) Total distance covered by the object. The total distance covered is the area under the speed-time graph. We can divide the graph into three sections: a triangle (0-4 s), a rectangle (4-10 s), and another triangle (10-15 s). Step 1: Calculate the distance covered in the first 4 seconds (triangle). S_1 = (1)/(2) × base × height S_1 = (1)/(2) × 4 s × 20 m/s S_1 = 40 m Step 2: Calculate the distance covered from 4 s to 10 s (rectangle). The duration is 10 s - 4 s = 6 s. The speed is constant at 20 m/s. S_2 = length × width S_2 = 6 s × 20 m/s S_2 = 120 m Step 3: Calculate the distance covered from 10 s to 15 s (triangle). The duration is 15 s - 10 s = 5 s. The initial speed is 20 m/s and the final speed is 0 m/s. S_3 = (1)/(2) × base × height S_3 = (1)/(2) × 5 s × 20 m/s S_3 = 50 m Step 4: Calculate the total distance. S_total = S_1 + S_2 + S_3 S_total = 40 m + 120 m + 50 m S_total = 210 m The total distance covered by the object is 210 m. c) Average speed in the last 4 seconds. The last 4 seconds of the motion are from t = 15 s - 4 s = 11 s to t = 15 s. Step 1: Determine the speed at t = 11 s and t = 15 s. At t = 15 s, the object comes to rest, so v_15 = 0 m/s. To find the speed at t = 11 s, we first calculate the deceleration in the last segment (10 s to 15 s). a_decel = final speed - initial speedtime interval a_decel = 0 m/s - 20 m/s15 s - 10 s a_decel = -20 m/s5 s = -4 m/s^2 Now, use v = u + at for the interval from t=10 s to t=11 s. Here, u = 20 m/s (speed at t=10 s), a = -4 m/s^2, and t = 11 s - 10 s = 1 s. v_11 = 20 m/s + (-4 m/s^2)(1 s) v_11 = 20 m/s - 4 m/s = 16 m/s Step 2: Calculate the average speed in the last 4 seconds. For uniformly changing speed, the average speed is initial speed + final speed2. v_avg = v_11 + v_152 v_avg = 16 m/s + 0 m/s2 v_avg = 16 m/s2 = 8 m/s The average speed in the last 4 seconds is 8 m/s. That's 2 down. 3 left today — send the next one.