Maharashtra Board Solutions for Chapter: Motion in a Plane, Exercise 2: Exercises

A velocity-time graph is shown in the adjoining figure.

Determine: (v) distance traveled by the car in first 6 sec.

A man throws a ball to a maximum horizontal distance of $80 \mathrm{meters}$. Calculate the maximum height reached.

A particle is projected with speed ${\mathrm{v}}_0$ at angle $\mathrm{\theta }$ to the horizontal on an inclined surface making an angle $\mathrm{\varphi }(\mathrm{\varphi }<\theta )$ to the horizontal. Find the range of the projectile along the inclined surface.

A metro train runs from station A to B to C. It takes $4 \mathrm{minutes}$ in travelling from station A to station B. The train halts at station B for$20 \mathrm{s}$. Then it starts from station B and reaches station C in next $3 \mathrm{minutes}$. At the start, the train accelerates for $10 \sec$ to reach the constant speed of $72 \mathrm{km}/\mathrm{hr}$. The train moving at the constant speed is brought to rest in $10 \sec$ at next station. (i) Plot ·the velocity-time graph for the train travelling from the station A to B to C. (ii) Calculate the distance between the stations A, Band C.

A train is moving eastward at $10 \mathrm{m}/\sec$. A waiter is walking eastward at $1.2\mathrm{m}/\sec$ and a fly is charging towards the north across the waiter's tray at $2 \min$. What is the velocity of the fly relative to Earth. 

A car moves in a circle at the constant speed of $50 \mathrm{m}/\mathrm{s}$  and completes one revolution in $40 \mathrm{s}$. Determine the magnitude of the acceleration of the car.

A particle moves in a circle with constant speed of $15 \mathrm{m}/\mathrm{s}$. The radius of the circle is $2 \mathrm{m}$. Determine the centripetal acceleration of the particle.

A projectile is thrown at an angle of $30°$ to the horizontal. What should be the range of initial velocity $\left(\mathrm{u}\right)$ so that its range will be between $40 \mathrm{m}$ and $50 \mathrm{m}$? Assume$\mathrm{g}=10 \mathrm{m}/{\mathrm{s}}^2$•