Equations of Motion

A car starting from rest accelerates uniformly to acquire a speed of $20 \mathrm{km} {\mathrm{h}}^{-1}$ in $30 \min$. The distance travelled by the car in this interval will be :

The correct equation of motion is :

Write an expression for the distance $S$ covered in time $t$ by a body which is initially at rest and starts moving with a constant acceleration $a$.

Write three equations of uniformly accelerated motion relating the initial velocity $\left(u\right)$, final velocity $\left(v\right)$, time $\left(t\right)$, acceleration $\left(a\right)$ and displacement $\left(s\right)$.

A train starts from rest and accelerates uniformly at a rate of $2 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$ for $10 s$. It then maintains a constant speed for $200 s$. The brakes are then applied and the train is uniformly retarded and comes to rest in $50 s$. Find the average velocity of the train.

A train starts from rest and accelerates uniformly at a rate of $2 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$ for $10 s$. It then maintains a constant speed for $200 s$. The brakes are then applied and the train is uniformly retarded and comes to rest in $50 s$. Find the total distance travelled by the train.

A train starts from rest and accelerates uniformly at a rate of $2 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$ for $10 s$. It then maintains a constant speed for $200 s$. The brakes are then applied and the train is uniformly retarded and comes to rest in $50 s$. Find the retardation in the last $50 s$.

A train starts from rest and accelerates uniformly at a rate of $2 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$ for $10 s$. It then maintains a constant speed for $200 s$. The brakes are then applied and the train is uniformly retarded and comes to rest in $50 s$. Find the maximum velocity reached.

A space craft flying in a straight course with a velocity of $75 \raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ fires its rocket motors for $6.0 s$. At the end of this time, its speed is $120 \raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ in the same direction. Find the distance travelled by the space craft in the first $10 s$ after the rocket motors were started, the motors having been in action for only $6.0 s$.

A space craft flying in a straight course with a velocity of $75 \raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ fires its rocket motors for $6.0 s$. At the end of this time, its speed is $120 \raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ in the same direction. Find the space craft's average acceleration while the motors were firing.

A car travels with a uniform velocity of $25 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ for $5 s$. The brakes are then applied and the car is uniformly retarded and comes to rest in further $10 s$. Find the distance travelled by the car after applying the brakes.

A car travels with a uniform velocity of $25 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ for $5 s$. The brakes are then applied and the car is uniformly retarded and comes to rest in further $10 s$. Find the retardation.

A car travels with a uniform velocity of $25 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ for $5 s$. The brakes are then applied and the car is uniformly retarded and comes to rest in further $10 s$. Find the distance which the car travels before the brakes are applied.

A body moving with a constant acceleration travels the distances $3 m$ and $8 m$ respectively in $1 s$ and $2 s$. Calculate the acceleration of body.

A body moving with a constant acceleration travels the distances $3 m$ and $8 m$ respectively in $1 s$ and $2 s$. Calculate the initial velocity of body.

A body moves from rest with a uniform acceleration and travels $270 m$ in $3 s$. Find the velocity of the body at $10 s$ after the start.

When brakes are applied to a bus, the retardation produced is $25 {\raisebox{1ex}{$cm$}\!\left/ \!\raisebox{-1ex}{$s$}\right.}^2$ and the bus takes $20 s$ to stop. Calculate the distance travelled by bus during this time.

When brakes are applied to a bus, the retardation produced is $25 \raisebox{1ex}{$cm$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$ and the bus takes $20 s$ to stop. Calculate the initial velocity of bus during this time.

A car travels a distance $100 m$ with a constant acceleration and average velocity of $20 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$. The final velocity acquired by the car is $25 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$. Find the acceleration of car.

A car travels a distance $100 m$ with a constant acceleration and average velocity of $20 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$. The final velocity acquired by the car is $25 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$. Find the initial velocity of car.