Mizoram Board Solutions for Chapter: Motion in a Plane, Exercise 1: EXERCISES

Given $\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}=0$, which of the following statements are correct:

The net acceleration of a particle in a circular motion is always along the radius of the circle towards the centre.

The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.

The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.

For any arbitrary motion in space, which of the following relations are true:

(Note: The word 'average' stands for average of the quantity over the time interval $t_1$ to $t_2$)

A cyclist is riding with a speed of $27 \mathrm{km}/\mathrm{h}$. As he approaches a circular turn on the road of radius $80 \mathrm{m}$, he applies brakes and reduces his speed at the constant rate of $0.50 \mathrm{m}/\mathrm{s}$ every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?

Show that for a projectile the angle between the velocity and the $x-$axis as a function of time is given by

$\theta \left(t\right)={\tan }^{-1}\left(\frac{v_{0y}-gt}{v_{0x}}\right)$

where the symbols have their usual meaning.

Shows that the projection angle ${\theta }_0$ for a projectile launched from the origin is given by