Question

Let $v$ and $a$ denote the velocity and acceleration respectively, of a body in one-dimensional motion. Then which among the following is true ?

• A. $\left|v\right|$ must decrease when $a<0$.
• B. Speed must increase when $a>0$.
• C. Speed will increase when both $v$ and $a<0$.
• D. Speed will decrease when $v<0$ and $a>0$.

Answer 1

Answer: (C), (D)

Speed will increase when both $v$ and $a<0$.
Speed will decrease when $v<0$ and $a>0$.

Option A is incorrect because there can be a case when the velocity is in negative direction, so the acceleration will increase the magnitude of the velocity.
Option B is incorrect because velocity and acceleration can be of opposite direction which will decrease the velocity.
Option C is correct because both velocity and acceleration have same direction so there will be an increase in magnitude of velocity.
Option D is correct because both acceleration and velocity are opposite in direction and there will be a decrease in magnitude of velocity.