R P Goyal and S P Tripathi Solutions for Chapter: Motion in One Dimension, Exercise 3: EXERCISE–2(C)

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 $\left(s\right)$.

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 $a$.

The correct equation of motion is :

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 :

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 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 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 average velocity of the train.