If a car accelerates uniformly from rest to a speed of 25 m/s in 10 seconds, wha

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Question: If a car accelerates uniformly from rest to a speed of 25 m/s in 10 seconds, what is the distance covered during this time? (2023)

Options:

Correct Answer: 125 m

Exam Year: 2023

Solution:

Distance = ut + (1/2)at². Here, u = 0, a = (25-0)/10 = 2.5 m/s². Distance = 0 + (1/2)(2.5)(10²) = 125 m.

If a car accelerates uniformly from rest to a speed of 25 m/s in 10 seconds, what is the distance covered during this time? (2023)

If a car accelerates uniformly from rest to a speed of 25 m/s in 10 seconds, what is the distance covered during this time? (2023)

Step 1: Identify the initial speed (u). Since the car starts from rest, u = 0 m/s.
Step 2: Identify the final speed (v). The car accelerates to a speed of 25 m/s.
Step 3: Identify the time (t) taken to reach the final speed. The time is given as 10 seconds.
Step 4: Calculate the acceleration (a) using the formula a = (v - u) / t. Here, a = (25 m/s - 0 m/s) / 10 s = 2.5 m/s².
Step 5: Use the formula for distance (s) covered during acceleration: s = ut + (1/2)at².
Step 6: Substitute the values into the distance formula. Since u = 0, the formula simplifies to s = (1/2)(2.5 m/s²)(10 s)².
Step 7: Calculate (10 s)², which is 100 s².
Step 8: Multiply (1/2) by 2.5 m/s² and 100 s²: (1/2)(2.5)(100) = 125 m.
Step 9: Conclude that the distance covered during the 10 seconds is 125 meters.

Uniform Acceleration – Understanding the equations of motion for an object accelerating uniformly from rest.
Kinematic Equations – Application of the kinematic equation to calculate distance, given initial velocity, acceleration, and time.