A car accelerates uniformly from rest to a speed of 25 m/s in 10 seconds. What i

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Question: A car accelerates uniformly from rest to a speed of 25 m/s in 10 seconds. What is the distance covered by the car during this time?

Options:

Correct Answer: 125 m

Solution:

Distance (s) = ut + (1/2)at^2. Here, a = (v-u)/t = (25-0)/10 = 2.5 m/s². So, s = 0 + (1/2)*2.5*10^2 = 125 m.

A car accelerates uniformly from rest to a speed of 25 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 25 m/s in 10 seconds. What is the distance covered by the car during this time?

Step 1: Identify the initial speed (u) of the car. Since the car starts from rest, u = 0 m/s.
Step 2: Identify the final speed (v) of the car. The car accelerates to a speed of 25 m/s, so v = 25 m/s.
Step 3: Identify the time (t) taken to reach the final speed. The time given is 10 seconds, so t = 10 s.
Step 4: Calculate the acceleration (a) of the car using the formula a = (v - u) / t. Substitute the values: a = (25 - 0) / 10 = 2.5 m/s².
Step 5: Use the formula for distance (s) covered during acceleration: s = ut + (1/2)at². Substitute the values: s = 0 * 10 + (1/2) * 2.5 * (10)².
Step 6: Calculate (1/2) * 2.5 * (10)². First, calculate (10)² = 100, then (1/2) * 2.5 * 100 = 125 m.
Step 7: Conclude that the distance covered by the car during this time is 125 meters.

Uniform Acceleration – The car accelerates uniformly, 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.
Calculating Acceleration – The calculation of acceleration from the change in velocity over time is a key concept in solving the problem.