Motion in a Plane

A car travels 4 km in a direction 45º east of north and then 2km in a direction 45º west of north. The distance travelled by the car is-

A train of 150 metre long is going towards north direction at a speed of 10m/s. A parrot flies at the speed of 5m/s towards south direction parallel to the railway track. The time taken by the parrot to cross the train is

If a body is projected with an angle $\theta$ to the horizontal, then

Which of the following graphs represents the position-time graph of a particle moving with negative velocity?

The angular speed of the minute hand of a clock in degrees per second is

Two objects are projected with same velocity 'u' at different angles $\alpha$ and $\beta$ with the horizontal. If $\alpha+\beta=90^{\circ}$, the ratio of horizontal range of the first object to the second object will be $[\sin (\pi-\theta)=\sin \theta]$

A particle is performing U.C.M. along a circle of radius $R$. In half the period of revolution, its displacement and distance covered are respectively

A constant force $\vec{F}=3 \hat{i}-2 \hat{j}-\hat{k}$ newton has a displacement $\vec{r}=2 \hat{i}-3 \hat{j}-3 \hat{k}$ metre in 2 second. The work done and the power are respectively

For a particle in uniform circular motion

Which of the following statements is incorrect?

An object is projected at an angle $\theta$ to the horizontal in a gravitational field and it follows a parabolic path PQRST. These points are the positions of the object after successive equal time intervals, $T$ being the highest point reached. The displacements $PQ,QR$ and $ST$

A boy throws a ball with a velocity $v_{0}$ at an angle $\alpha$ to the ground. At the same instant he starts running with uniform velocity to catch the ball before it hits the ground. To achieve this, he should run with a velocity of

A train of 150 metre length is going towards north direction at a speed of $10 \mathrm{m}/\mathrm{s}$. A parrot flies at the speed of $5 \mathrm{m}/\mathrm{s}$ towards south direction parallel to the railways track. The time taken by the parrot to cross the train is

The displacement-time graphs of two moving particles make angles of ${30}^{\circ}$ and ${45}^{\circ}$ with the $x$-axis as shown in the figure. The ratio of their respective velocity is

A boat is moving with a velocity $3\overset{\hat{}}{i}+4\overset{\hat{}}{j}$ m/s w.r.t. ground. The water in the river is moving with a velocity $-3\overset{\hat{}}{i}-4\overset{\hat{}}{j}$ m/s w.r.t. ground. The relative velocity of the boat w.r.t. water is