A cyclist starts from the centre O of a circu | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The net displacement of the cyclist is $0 	ext{ m}$,since the initial position coincides with the final position (the centre $O$).The total dista

Vedclass · Accepted Answer

$0, 21.4$

Vedclass · Answer

(D) The net displacement of the cyclist is $0 	ext{ m}$,since the initial position coincides with the final position (the centre $O$).The total distance travelled is the sum of the paths $OP$,$PQ$ (arc length),and $QO$.$OP = 1 	ext{ km}$,$QO = 1 	ext{ km}$.Since $O$ is the centre and $OP$ and $OQ$ are perpendicular radii,the arc $PQ$ corresponds to a quarter of the circumference: $PQ = \frac{1}{4} 	imes (2\pi r) = \frac{1}{4} 	imes 2 	imes \pi 	imes 1 = \frac{\pi}{2} 	ext{ km}$.Total distance $= 1 + \frac{\pi}{2} + 1 = 2 + \frac{\pi}{2} = \frac{4 + \pi}{2} 	ext{ km}$.Total time $= 10 	ext{ minutes} = \frac{10}{60} 	ext{ hours} = \frac{1}{6} 	ext{ hours}$.Average speed $= \frac{	ext{Total distance}}{	ext{Total time}} = \frac{(4 + \pi)/2}{1/6} = \frac{4 + \pi}{2} 	imes 6 = 3(4 + \pi) 	ext{ km/h}$.Using $\pi \approx 3.14$,Average speed $= 3(4 + 3.14) = 3(7.14) = 21.42 	ext{ km/h} \approx 21.4 	ext{ km/h}$.Thus,the displacement is $0 	ext{ m}$ and the average speed is $21.4 	ext{ km/h}$.

Similar Questions

If two bodies $A$ and $B$ are projected with the same velocity $u$ but with different angles $\theta_1$ and $\theta_2$ respectively with the horizontal such that both have the same range,then the ratio of the times of flight of the bodies $A$ and $B$ is:

The initial velocity of a projectile is $\vec{u} = (4\hat{i} + 3\hat{j})\,m/s$. It is moving with uniform acceleration $\vec{a} = (0.4\hat{i} + 0.3\hat{j})\,m/s^2$. The magnitude of its velocity after $10\,s$ is.........$m/s$.

$A$ body is moving with velocity $30 \; m/s$ towards east. After $10 \; s$,its velocity becomes $40 \; m/s$ towards north. The average acceleration of the body is ...... $m/s^2$.

$A$ stone is projected with a velocity $20 \sqrt{2} \, m/s$ at an angle of $45^{\circ}$ to the horizontal. The average velocity of the stone during its motion from the starting point to its maximum height is $.......... \, m/s$ (take $g = 10 \, m/s^2$).

$A$ boy throws a ball with a velocity $V_0$ at an angle $\alpha$ to the ground. At the same time,he starts running with a uniform velocity to catch the ball before it hits the ground. To achieve this,he should run with a velocity of

Vedclass Test Series

Exam Paper Generator

Online Exam Module