Exercise-2

Two balls are dropped from different heights. One ball is dropped $2 \sec$ after the other but they both strike the ground at the same time, $3 \sec$ after the first is dropped. The difference in the heights at which they were dropped is

The distance $\left(x\right)$ travelied by a particle in time $t$, is given by $t=2x^2+3x.$ If $\text{'}v\text{'}$ is the velocity. Then acceleration will be

Assertion : A particle having negative acceleration will slow down.

Reason : Direction of the acceleration is dependent upon direction of the velocity.

Assertion : Magnitude of average velocity is equal to average speed.

Reason : Magnitude of instantaneous velocity is not equal to instantaneous speed.

Assertion : When velocity of a particle is zero then acceleration of particle must be zero at that instant.

Reason : Acceleration is equal to $a=\left(\frac{dv}{dx}\right),$ where $v$ is the velocity at that instant.

Assertion : A particle moves in a straight line with constant acceleration. The average velocity of this particle cannot be zero in any time interval.

Reason : For a particle moving in straight line with variable acceleration, the average velocity in a time interval is $\frac{u+v}{2},$ where $u$ and $v$ are initial and final velocity of the particle in the given time interval.

Assertion : For a particle moving in a straight line, velocity ($v$ in ${\mathrm{ms}}^{-1}$) of the particle-in terms of time ($t$ in $\sec$ ) is given by,  $v=t^2-6t+8.$Then the speed of the particle is minimum at $t=2 \sec .$ Reason : For a particle moving in a straight line the velocity $v$ at any time $t$ may be minimum or may be maximum when $\frac{dv}{dt}=0.$

Assertion : Retardation is directly opposite to the velocity.

Reason : Retardation is equal to the time rate of decrease of speed.