This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Answer
50 s
Here are the solutions based on the velocity-time graph:
i) The total time taken for the journey. Step 1: Identify the final time value on the x-axis. The graph starts at s and ends at s. The total time taken is .
ii) The maximum velocity reached. Step 1: Identify the highest point on the y-axis (velocity axis) that the graph reaches. The highest velocity shown on the graph is 30 m/s. The maximum velocity reached is .
iii) The acceleration during the first 20 seconds. Step 1: Recall that acceleration is the gradient of a velocity-time graph. The acceleration is given by the formula . Step 2: Identify the initial and final velocities and times for the first 20 seconds. Initial velocity () at s is 0 m/s. Final velocity () at s is 30 m/s. Step 3: Substitute the values into the formula and calculate. The acceleration during the first 20 seconds is .
iv) The total distance travelled. Step 1: Recall that the total distance travelled is the area under the velocity-time graph. The shape under the graph is a trapezoid. The area of a trapezoid is given by , where and are the lengths of the parallel sides and is the height. Step 2: Identify the lengths of the parallel sides and the height from the graph. The parallel sides are the time intervals where the velocity is non-zero. Length of the top parallel side (constant velocity section): . Length of the bottom parallel side (total time): . The height of the trapezoid (maximum velocity) is 30 m/s. Step 3: Substitute the values into the formula and calculate. The total distance travelled is .
That's 2 down. 3 left today — send the next one.
Get instant step-by-step solutions to any question. Free to start.
Ask Your Question
Handwritten Step-by-Step Solution
Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.
Try on WhatsAppStill have questions?
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.