Mark the correct statements for a particle going on a straight line
if the position and velocity have opposite sign, the particle is moving towards the origin
if the velocity is zero for a time interval, the acceleration is zero at any instant within the time interval
if the velocity and acceleration have opposite sign, the object is slowing down
All of the above
The engine of a motorcycle can produce a maximum acceleration $5 \,ms^{-2}$. Its brakes can produce a maximum retardation $10\, ms^{-2}$. What is the minimum time in which it can cover a distance of $1.5\, km$.........$sec$
The velocity $(v)$-time $(t)$ graph for a particle moving along $x$-axis is shown in the figure. The corresponding position $(x)$ - time $(t)$ is best represented by
The acceleration of a train between two stations is shown in the figure. The maximum speed of the train is $............\,m/s$
Stopping distance of vehicles : When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity $(v_0)$ and the braking capacity, or deceleration, $-a$ that is caused by the braking. Derive an expression for stopping distance of a vehicle in terms of $v_0 $ and $a$.
A particle is moving in a straight line with initial velocity and uniform acceleration $a$. If the sum of the distance travelled in $t^{\text {th }}$ and $( t +1)^{ th }$ seconds is $100 cm$, then its velocity after $t$ seconds, in $.........cm / s$, is