A car accelerates uniformly from rest to a speed of 20 m/s in 10 seconds. What is the distance covered by the car during this time?
Practice Questions
1 question
Q1
A car accelerates uniformly from rest to a speed of 20 m/s in 10 seconds. What is the distance covered by the car during this time?
100 m
200 m
300 m
400 m
Using the formula: distance = initial velocity * time + 0.5 * acceleration * time^2. Here, initial velocity = 0, final velocity = 20 m/s, time = 10 s. Acceleration = (final velocity - initial velocity) / time = 2 m/s². Distance = 0 + 0.5 * 2 * 10² = 100 m.
Questions & Step-by-step Solutions
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Q
Q: A car accelerates uniformly from rest to a speed of 20 m/s in 10 seconds. What is the distance covered by the car during this time?
Solution: Using the formula: distance = initial velocity * time + 0.5 * acceleration * time^2. Here, initial velocity = 0, final velocity = 20 m/s, time = 10 s. Acceleration = (final velocity - initial velocity) / time = 2 m/s². Distance = 0 + 0.5 * 2 * 10² = 100 m.
Steps: 8
Step 1: Identify the initial velocity of the car. Since the car starts from rest, the initial velocity is 0 m/s.
Step 2: Identify the final velocity of the car. The final velocity is given as 20 m/s.
Step 3: Identify the time taken for the acceleration. The time is given as 10 seconds.
Step 4: Calculate the acceleration using the formula: acceleration = (final velocity - initial velocity) / time. Plug in the values: acceleration = (20 m/s - 0 m/s) / 10 s = 2 m/s².
Step 5: Use the distance formula: distance = initial velocity * time + 0.5 * acceleration * time². Since the initial velocity is 0, the formula simplifies to distance = 0 + 0.5 * acceleration * time².
Step 6: Plug in the values for acceleration and time: distance = 0.5 * 2 m/s² * (10 s)².
Step 7: Calculate (10 s)², which is 100 s².
Step 8: Now calculate the distance: distance = 0.5 * 2 * 100 = 100 m.
