Question

if v is velocity of a particle moving in a straight line and a is acceleration of the particle ,then the speed of particle would be decreasing if​

Answer 1

Answer:

if v is velocity of particle moving in straight line and a acceleration of particle and speed of particle is increases

Answer 2

The speed of the particle will be decreasing when the acceleration vector is opposite to the direction of velocity vector.

for example: if direction of velocity vector is i cap then the direction of acceleration vector will be negative i cap.

And if two vector are in opposite direction then the angle made between them is 180°, and the dot product of the two vector will always be negative.

the reason why the answer will be negative is given below.

a vector • v vector = |a| |v| cos180°

a vector • v vector = |a| |v| (-1) {cos180° = -1}

here |a| is always positive, |v| is always positive but -1 is negative so the final answer will always be negative in this case.

therefore a vector • v vector will be less than 0.