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General SciencePhysics: Motion
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A motorcycle increases its speed from 10 m/s to 30 m/s in 4 seconds. Find the acceleration of the motorcycle.

A

5 m/s┬▓

B

10 m/s┬▓

C

2.5 m/s┬▓

D

8 m/s┬▓

Correct Answer

ЁЯФм SC тАв Science Concept & PrincipleGeneral SciencePhysics: Motion
Option A

5 m/s┬▓

Quick Summary:

Acceleration is defined as the rate of change of velocity per unit time. By calculating the difference between the final velocity (30┬аm/s30 \text{ m/s}30┬аm/s) and initial velocity (10┬аm/s10 \text{ m/s}10┬аm/s) and dividing it by the time interval (4┬аs4 \text{ s}4┬аs), we get the acceleration value of 5┬аm/s25 \text{ m/s}^25┬аm/s2.

ЁЯФмSCScience SolutionConcept & Principle
ЁЯТб Explanation

Acceleration is defined as the rate of change of velocity per unit time. By calculating the difference between the final velocity (30┬аm/s30 \text{ m/s}30┬аm/s) and initial velocity (10┬аm/s10 \text{ m/s}10┬аm/s) and dividing it by the time interval (4┬аs4 \text{ s}4┬аs), we get the acceleration value of 5┬аm/s25 \text{ m/s}^25┬аm/s2.

ЁЯТб Everyday Analogy (Real-World Intuition)

Think of it as stepping on the accelerator of a car; the 'kick' you feel in your seat is proportional to how quickly your speed increases, which is your acceleration.

ЁЯза Memory Mnemonic / Shortcut Aid

Remember 'V-U over T' (Velocity final minus Initial, over Time).

ЁЯФв Key Formulas

a=vтИТuta = \frac{v - u}{t}a=tvтИТuтАЛ тАФ formula for acceleration where aaa is acceleration, vvv is final velocity, uuu is initial velocity, and ttt is time.

тЪЩя╕П Working Principle

Acceleration is governed by Newton's laws of motion. It represents the vector change in velocity. The formula a=vтИТuta = \frac{v - u}{t}a=tvтИТuтАЛ calculates the uniform acceleration when the change in velocity is constant over a given time duration.

ЁЯУМ Key Points
  • тЦ╕

    Acceleration is a vector quantity, meaning it has both magnitude and direction.

  • тЦ╕

    The SI unit for acceleration is m/s2\text{m/s}^2m/s2.

  • тЦ╕

    If acceleration is constant, the velocity-time graph will be a straight line.

тЬЕ Advantages
  • тЦ╕

    Uniform acceleration allows for predictable motion calculations.

тЭМ Disadvantages / Limitations
  • тЦ╕

    Real-world motorcycle acceleration is rarely perfectly constant.

ЁЯЫая╕П Applications / Uses
  • тЦ╕

    Design of automotive engines for performance metrics.

  • тЦ╕

    Analysis of traffic flow and road safety dynamics.

ЁЯУД Additional Information
  • тЦ╕

    Initial velocity (uuu) = 10┬аm/s10 \text{ m/s}10┬аm/s, Final velocity (vvv) = 30┬аm/s30 \text{ m/s}30┬аm/s, Time (ttt) = 4┬аs4 \text{ s}4┬аs. Calculation: a=30тИТ104=204=5┬аm/s2a = \frac{30 - 10}{4} = \frac{20}{4} = 5 \text{ m/s}^2a=430тИТ10тАЛ=420тАЛ=5┬аm/s2.

  • тЦ╕

    Option B (10┬аm/s210 \text{ m/s}^210┬аm/s2) is incorrect because the numerator 202020 divided by 444 is 555, not 101010.

ЁЯУК Diagram / Illustration
Acceleration Calculation 1 Given Data u = 10 m/s, v = 30 m/s, t = 4 s 2 Formula a = (v - u) / t 3 Calculation a = (30 - 10) / 4 = 20 / 4 = 5 m/s┬▓ 4 Final Result Acceleration = 5 m/s┬▓ Correct Option: A) 5 m/s┬▓
тЬЕ

A is correct тАФ The acceleration of the motorcycle is calculated as 5┬аm/s25 \text{ m/s}^25┬аm/s2.

Core Concepts Used
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Kinematics Newtonian Mechanics Uniform Acceleration
ЁЯТб EXAM TIP

Always ensure your units are consistent (m, s, m/s) before applying kinematic equations to avoid calculation errors.

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