A vehicle accelerates from rest to a speed of 36 m/s in 12 seconds. What is the

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Question: A vehicle accelerates from rest to a speed of 36 m/s in 12 seconds. What is the distance covered during this time? (2023)

Options:

Correct Answer: 144 m

Exam Year: 2023

Solution:

Using the formula s = ut + (1/2)at², where a = (v-u)/t = (36-0)/12 = 3 m/s², we find s = 0 + (1/2)(3)(12²) = 216 m.

A vehicle accelerates from rest to a speed of 36 m/s in 12 seconds. What is the distance covered during this time? (2023)

A vehicle accelerates from rest to a speed of 36 m/s in 12 seconds. What is the distance covered during this time? (2023)

Step 1: Identify the initial speed (u) of the vehicle. Since the vehicle starts from rest, u = 0 m/s.
Step 2: Identify the final speed (v) of the vehicle. The final speed is given as v = 36 m/s.
Step 3: Identify the time (t) taken to reach the final speed. The time is given as t = 12 seconds.
Step 4: Calculate the acceleration (a) using the formula a = (v - u) / t. Substitute the values: a = (36 - 0) / 12 = 3 m/s².
Step 5: Use the formula for distance (s) covered during acceleration: s = ut + (1/2)at². Substitute the values: s = 0 * 12 + (1/2)(3)(12²).
Step 6: Calculate (1/2)(3)(12²). First, calculate 12² = 144, then (1/2)(3)(144) = (1.5)(144) = 216 m.
Step 7: Conclude that the distance covered during the 12 seconds is 216 meters.

Kinematics – The study of motion, specifically how objects move under the influence of forces, including concepts of acceleration, velocity, and distance.
Equations of Motion – The use of equations that relate displacement, initial velocity, final velocity, acceleration, and time to solve problems involving linear motion.