A woman starts from her home at $9.00\; \mathrm{am}$, walks with a speed of $5\; \mathrm{km} h^{-1}$ on a straight road up to her office $2.5\; \mathrm{km}$ away, stays at the office up to $5.00 \;\mathrm{pm}$, and returns home by an auto with a speed of $25\; \mathrm{km} h^{-1}$. Choose suitable scales and plot the $x -t$ graph of her motion

The motion of a particle is described by the equation $u = at$. The distance travelled by the particle in the first $4$ seconds

Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by $ x_p(t)=at+bt^2 $ and $x_Q(t)= ft- t^2$. At what time do the cars have the same velocity $?$ 

Two small blocks slide without losing contact with the surface along two frictionless tracks $1$ and $2$ , starting at the same time with same initial speed $v$. Track $1$ is perfectly horizontal, while track $2$ has a dip in the middle, as shown in the figure.Which block reaches the finish line first?[Hint: Use velocity-time graph to solve]

Match Column$-I$ with Column$-II :$

Choose the correct answer from the options given below: