A cyclist accelerates from rest at a rate of 1 m/s². How far will he travel in 10 seconds?

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Q: A cyclist accelerates from rest at a rate of 1 m/s². How far will he travel in 10 seconds?

Solution: Using the formula: distance = initial velocity * time + 0.5 * acceleration * time². Distance = 0 + 0.5 * 1 * 10² = 50 m.

Steps: 7

Step 1: Identify the initial velocity of the cyclist. Since the cyclist starts from rest, the initial velocity is 0 m/s.
Step 2: Identify the acceleration of the cyclist. The problem states that the acceleration is 1 m/s².
Step 3: Identify the time duration for which the cyclist accelerates. The time given is 10 seconds.
Step 4: Use the formula for distance: distance = initial velocity * time + 0.5 * acceleration * time².
Step 5: Substitute the values into the formula: distance = 0 * 10 + 0.5 * 1 * (10)².
Step 6: Calculate the second part of the formula: 0.5 * 1 * (10)² = 0.5 * 1 * 100 = 50.
Step 7: Since the first part (initial velocity * time) is 0, the total distance traveled is 50 meters.