A motor car moving with velocity $7 \mathrm{~m} / \mathrm{s}$ stops at 10 m distance when brakes are applied. What is the relation between the resistance force $R$ and the weight $w$ of the car? (take, value of $g=9.8 \mathrm{~m} / \mathrm{s}^2$ )

A block is placed on a parabolic shape ramp given by equation, $y=\frac{x^2}{20}$. If the coefficient of static friction $\left(\mu_s\right)$ is 0.5 , then what is the maximum height above the ground at which the block can be placed without slipping?

Two blocks of masses 1 kg and 2 kg connected by a light rod and the system is slipping down a rough incline angle $45^{\circ}$ with the horizontal. The frictional coefficient at both the contacts is 0.4 . If the acceleration of the system is $\alpha \sqrt{2}$, the value of $\alpha$ is (use, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A time varying force acts on a ball of mass 100 g for 2 ms . The force versus time curve is shown below. If the initial speed of the ball is $10 \mathrm{~m} / \mathrm{s}$, then the speed of ball after 2 ms is