A particle starts moving with acceleration $2 \,m / s ^2$. Distance travelled by it in $5^{\text {th }}$ half second is ....... $m$

The relation between time $t$ and distance $x$ for a moving body is given as $t=m x^{2}+n x$, where ${m}$ and ${n}$ are constants. The retardation of the motion is -

(Where $v$ stands for velocity)

A uniformly moving cricket ball is turned back by hitting it with a bat for a very short time interval. Show the variation of its acceleration with time (Take acceleration in the backward direction as positive).

What will be change in speed of moving object if both speed and acceleration are positive or negative ?

Read each statement below carefully and state with reasons and examples, if it is true or false 

A particle in one-dimensional motion

$(a)$ with zero speed at an instant may have non-zero acceleration at that instant

$(b)$ with zero speed may have non-zero velocity.

$(c)$ with constant speed must have zero acceleration.

$(d)$ with positive value of acceleration must be speeding up.

The velocity-time graphs of a car and a scooter are shown in the figure. $(i)$ the difference between the distance travelled by the car and the scooter in $15\, s$ and $(ii)$ the time at which the car will catch up with the scooter are, respectively