21. Rohit completes a semi circular path of radius R in 10 seconds. Calculate average speed and average velocity in m/s.
A. \(\frac{2\pi R}{10},\frac{2R}{10}\)
B. \(\frac{\pi R}{10},\frac{R}{10}\)
C. \(\frac{\pi R}{10},\frac{2R}{10}\)
D. \(\frac{2\pi R}{10},\frac{R}{10}\)
Answer : Option C
22. A particle moves 4m in the south direction. Then it moves 3m in the west direction. The time taken by the particle is 2 second. What is the ratio between average speed and average velocity ?
A. \(\frac{5}{7}\)
B. \(\frac{7}{5}\)
C. \(\frac{14}{5}\)
D. \(\frac{5}{14}\)
Answer : Option B
23. A particle is projected vertically upwards with velocity 30 m/s. Find the ratio of average speed and instantaneous velocity after 6 s. \(\left [ g=10\ ms^{-2} \right ]\)
24. The motion of a particle along a straight line is described by the function \(x=\left ( 3t-2 \right )^{2}\). Calculate the acceleration after 10s.
A. \(9\ ms^{-2}\)
B. \(18\ ms^{-2}\)
C. \(36\ ms^{-2}\)
D. \(6\ ms^{-2}\)
Answer : Option B
Explanation :
\(v=\frac{\mathrm{d} x}{\mathrm{d} t}\) and \(a=\frac{\mathrm{d} v}{\mathrm{d} t}\)
Given figure shows a graph at acceleration \(\rightarrow \) time for a rectilinear motion. Find averageacceleration in first 10 seconds.
A. \(10\ ms^{-2}\)
B. \(15\ ms^{-2}\)
C. \(7.5\ ms^{-2}\)
D. \(30\ ms^{-2}\)
Answer : Option C
26. A body starts its motion with zero velocity and its acceleration is \(3\ ms^{-2}\). Find the distance traveled by it in fifth second.
27. A body is moving in x direction with constant acceleration \(\alpha \). Find the difference of the displacement covered by it in nth second and \((n-1)^{th}\) second.
A. \(\alpha \)
B. \(\frac{\alpha }{2}\)
C. \(3\alpha \)
D. \(\frac{3\alpha }{2}\)
Answer : Option A
28. What does the speedometer measure kept in motorbike ?
A. Average velocity
B. Average speed
C. Instantaneous speed
D. Instantaneous velocity
Answer : Option C
29. The displacement of a particle in x direction is given by \(x=9-5t+4t^{2}\). Find the velocity at time \(t = 0\)
30. A freely falling particle covers a building of 45m height in one second. Find the height of the point from where the particle was released. \(\left [ g=10\ ms^{-2} \right ]\)