Question

Throughout a time interval, while the speed of a particle increases as it moves along the x-axis, its velocity and acceleration might be

• A. positive and negative, respectively
• B. positive and positive, respectively
• C. negative and negative, respectively
• D. negative and positive, respectively

Answer 1

Answer: (B), (C)

negative and negative, respectively

The explanation for the correct options:

Option B:

1. If the speed of a particle is increasing along the positive x-axis so velocity will be positive along the x-axis and acceleration should also be positive because $\mathit{v}\mathbf{=}\mathit{u}\mathbf{+}\mathit{a}\mathit{t}$ according to the equation of motion.

Option C:

1. If the speed of a particle is increasing along the negative x-axis so velocity will be negative along the x-axis and acceleration should also be negative because $\mathbf{-}\mathit{v}\mathbf{=}\mathit{u}\mathbf{-}\mathit{a}\mathit{t}$ in this case resulting in an increasing speed.

The explanation for incorrect option:

Option A:

1. If the speed of a particle is increasing along the positive x-axis so velocity will be positive along the x-axis and if acceleration will be negative then $\mathit{v}\mathbf{=}\mathit{u}\mathbf{-}\mathit{a}\mathit{t}$ according to the equation of motion.
2. $\mathit{v}\mathbf{=}\mathit{u}\mathbf{-}\mathit{a}\mathit{t}$ equation clearly depicts that speed is decreasing along the positive x-axis. Hence, the acceleration can not be negative in this scenario.

Option D:

1. If the speed of a particle is increasing along the negative x-axis so velocity will be the negative along the x-axis and if acceleration will be positive then $\mathbf{-}\mathit{v}\mathbf{=}\mathit{u}\mathbf{+}\mathit{a}\mathit{t}$ according to the equation of motion.
2. $\mathbf{-}\mathit{v}\mathbf{=}\mathit{u}\mathbf{+}\mathit{a}\mathit{t}$ equation clearly depicts that speed is decreasing along the positive x-axis. Hence, the acceleration can not be positive in this scenario.

Thus, the correct options are B and C.