Question

Let v and a denote the velocity and acceleration respectively of a body in one dimensional motion.Then which of the statements are correct?

A) speed must decrease when a<0

B)speed must increase when a>0

C)speed will increase when both v and a are less than zero

D)speed will decrease when v<0 and a>0

It is a multi correct question

Answer 1

let us check each options
a)if acceleration is less than zero velocity will be decreasing but this does not mean that speed must decrease.suppose if we take a direction as positive .if the body is moving at an increasing speed opposite to this direction.then as speed increases the velocity become more negative and so will be the accelearation so this means EVEN IF ACCELERATION IS <0 SPEED MAY INCREASE AND HENCE THIS OPTION IS INCORRECT
b)suppose that the velocity of a body is -5 m/s then speed =5m/s(THE BODY IS TRAVELLING ALONG THE NEGATIVE DIRECTION)
at the next second it becomes 0 m/s speed will also be o m/s(THE BODY HAS COME TO REST)
then the acceleration will be (v-u/t)=0-(-5)/1=5m (s^-2)
here ACCELERATION IS POSITIVE BUT SPEED HAS BEEN REDUCED FROM 5 TO 0 SO THIS MEANS EVEN WHEN ACCELEARTION IS POSITIVE SPEED MAY DECREASE SO THIS OPTION IS ALSO WRONG
C)the scenario of this option is that the body is travelling in the negative direction and the acceleration is less than zero.
a=(v-u)/t if a<0 v-u<0( V IS FINAL VELOCITY AND u is initial velocity)
v<u
u is alraedy negative so v will be more negative
hence |v|>|u|
that is final speed greater than initial speed hence speed must increarse
SO SPEED WILL INCREASE IF BOT a AND v ARE NEGATIVE HENCE THIS OPTION IS TRUE
D)the scenario of this option is the body is travelling in the negative direction .
if a>o
v-u>0 v>u
but as u is negative
|v|<|u|
hence final speed is less than initial speed and this means that WHEN a>0 and v<0 speed will decrease HENCE THIS OPTION IS TRUE