$A$ driver applies the brakes on seeing the red traffic signal $400 \ m$ ahead. At the time of applying brakes,the vehicle was moving with $15 \ m/s$ and retarding at $0.3 \ m/s^2$. The distance of the vehicle from the traffic light one minute after the application of brakes is: (in $m$)

$A$ particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x^2 = 1 + t^2$. Its acceleration at any time $t$ is $x^{-n}$ where $n = . . . . .$

The displacement of a particle moving in a straight line is given by the expression $x = A t^3 + B t^2 + C t + D$ in metres, where $t$ is in seconds and $A, B, C$ and $D$ are constants. The ratio between the initial acceleration and initial velocity is

$A$ $150 \,m$ long train is moving with a uniform velocity of $45 \,km/h$. The time taken by the train to cross a bridge of length $850 \,m$ is..........$sec$.

The velocity of a car travelling on a straight road is $3.6 \ km/h$ at an instant of time. Now, travelling with uniform acceleration for $10 \ s$, the velocity becomes exactly double. If the wheel radius of the car is $25 \ cm$, then which of the following is the closest to the number of revolutions that the wheel makes during this $10 \ s$?

$A$ particle moves in a straight line with a constant acceleration. It changes its velocity from $10 \, m/s$ to $20 \, m/s$ while passing through a distance of $135 \, m$ in $t$ seconds. The value of $t$ is..........$s$.