A runner accelerates from rest to a speed of 10 m/s in 5 seconds. What is the to

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Question: A runner accelerates from rest to a speed of 10 m/s in 5 seconds. What is the total distance covered during this time?

Options:

Correct Answer: 12.5 m

Solution:

Using the formula d = 0.5 * a * t², first find a = (v_f - v_i) / t = (10 - 0) / 5 = 2 m/s². Then, d = 0.5 * 2 * (5)² = 25 m.

A runner accelerates from rest to a speed of 10 m/s in 5 seconds. What is the total distance covered during this time?

A runner accelerates from rest to a speed of 10 m/s in 5 seconds. What is the total distance covered during this time?

Step 1: Identify the initial speed (v_i) of the runner. Since the runner starts from rest, v_i = 0 m/s.
Step 2: Identify the final speed (v_f) of the runner. The final speed is given as v_f = 10 m/s.
Step 3: Identify the time (t) taken to reach the final speed. The time is given as t = 5 seconds.
Step 4: Calculate the acceleration (a) using the formula a = (v_f - v_i) / t. Substitute the values: a = (10 - 0) / 5 = 2 m/s².
Step 5: Use the formula for distance (d) covered during acceleration: d = 0.5 * a * t². Substitute the values: d = 0.5 * 2 * (5)².
Step 6: Calculate (5)² which is 25. Then, calculate d = 0.5 * 2 * 25.
Step 7: Multiply 0.5 * 2 to get 1. Then multiply 1 * 25 to get the total distance covered: d = 25 m.

Kinematics – The study of motion, specifically how objects move under the influence of forces, including concepts of acceleration, velocity, and distance.
Acceleration – The rate of change of velocity of an object, calculated as the change in velocity divided by the time taken.
Distance Calculation – Using kinematic equations to determine the distance traveled by an object under uniform acceleration.