A cyclist accelerates from rest at a rate of 1 m/s². How far will he travel in 8

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Question: A cyclist accelerates from rest at a rate of 1 m/s². How far will he travel in 8 seconds?

Options:

Correct Answer: 48 m

Solution:

Using the formula: distance = initial velocity * time + 0.5 * acceleration * time². Distance = 0 + 0.5 * 1 * 8² = 32 m.

A cyclist accelerates from rest at a rate of 1 m/s². How far will he travel in 8 seconds?

A cyclist accelerates from rest at a rate of 1 m/s². How far will he travel in 8 seconds?

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 8 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 * 8 + 0.5 * 1 * (8)².
Step 6: Calculate (8)², which is 64.
Step 7: Multiply 0.5 by 1 and then by 64: 0.5 * 1 * 64 = 32.
Step 8: Since the initial velocity part is 0, the total distance traveled is 32 meters.

Kinematics – The study of motion, specifically how objects move under the influence of forces, including concepts like acceleration, velocity, and distance.
Equations of Motion – The use of mathematical formulas to relate distance, velocity, acceleration, and time in uniformly accelerated motion.