Suppose a and 𝐯 denotes the acceleration and velocity...

Suppose a and $\mathbf{v}$ denotes the acceleration and velocity respectively of a body in one dimensional motion, then
(a) speed must increase when $a>0$
(b) speed will increase when $v$ and $d$ are $>0$
(c) speed must decreases when $a<0$
(d) speed will decrease when $v<0$ and $a>0$

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Key Concepts

Speed

Speed is the scalar magnitude of the velocity, meaning it is always a non-negative number that reflects how fast an object is moving regardless of its direction. Changes in speed depend on the alignment of acceleration with respect to velocity: if they are in the same direction, speed increases; if they are in opposite directions, speed decreases.

Acceleration

Acceleration is the rate at which the velocity of an object changes over time and is also a vector. In one-dimensional motion, it can either increase or decrease the speed of the object depending on whether it is in the same or opposite direction to the velocity.

Velocity

Velocity is a vector quantity that represents the rate of change of an object's position with respect to time and includes both magnitude and direction. Its sign indicates the direction of motion along a straight line, and its value can change when the object accelerates or decelerates.

One-Dimensional Motion

One-dimensional motion refers to movement along a single straight line where both velocity and acceleration can be described by scalar numbers with appropriate signs indicating direction. It simplifies analysis because all vector quantities reduce to one positive or negative value.

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