A car accelerates uniformly from rest to a speed of 20 m/s in 10 seconds. What i

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?

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?

Correct Answer: 100 m

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.

Uniform Acceleration – The car accelerates uniformly from rest, meaning its acceleration is constant over the time period.
Kinematic Equations – The question tests the application of kinematic equations to find distance when initial velocity, final velocity, and time are known.
Calculation of Acceleration – The calculation of acceleration from the change in velocity over time is a key concept in solving the problem.