41. The intercept of the velocity-time graph on the velocity axis gives.
A. initial velocity
B. final velocity
C. average velocity
D. instanteneous velocity
Answer : Option A
Here are the graphs of velocity \(\rightarrow \) time of two cars A and B, Find the ratio of the acceleration after time t.
A. \(\frac{1}{\sqrt{3}}\)
B. \(\frac{1}{3}\)
C. \(\sqrt{3}\)
D. \(3\)
Answer : Option B
Explanation :
acceleration = slope = tanθ
Here is a velocity - time graph of a motorbike moving in one direction. Calculate the distance covered by it in last two seconds.
In the figure acceleration (a) \(\alpha \) time (t) graph is given. Hence V \(\alpha \) ____
A. \(a\)
B. \(\sqrt{a}\)
C. \(a^{2}\)
D. \(a^{3}\)
Answer : Option C
Explanation :
\(\frac{\mathrm{d} a}{\mathrm{d} t}=constant\)
\(\therefore \frac{\mathrm{d} a}{\mathrm{d} v}.\frac{\mathrm{d} v}{\mathrm{d} t}=k\)
\(\therefore \frac{\mathrm{d} a}{\mathrm{d} v}=\frac{k}{a}\)
\(\therefore \int a\mathrm{d}a=\int k\mathrm{d}v\)
\(\therefore \frac{a^{2}}{2}=kv\)
The graph of displacement (x) \(\rightarrow \) time (t) for an object is given in the figure. In which part of the graph the acceleration of the particle is positive ?
A. OA
B. AB
C. O - A - B
D. acceleration is not positive at any part.
Answer : Option D
Explanation :
\(a=\frac{\mathrm{d}^{2} x}{\mathrm{d} t^{2}}\)
46. In a uniformly accelerated motion the slope of velocity - time graph gives _____
A. The instantaneous velocity
B. The acceleration
C. The initial velocity
D. The final velocity
Answer : Option B
47. The area covered by the curve of v – t graph and time axis is equal to magnitude of ____
A. change in velocity
B. change in acceleration
C. displacement
D. final velocity
Answer : Option C
48. An object moves in a straight line. It starts from the rest and its acceleration is \(2\ ms^{-2}\). After reaching a certain point it comes back to the original point. In this movement its acceleration is \(-3\ ms^{-2}\). till it comes to rest. The total time taken for the movement is 5 second. Calculate the maximum velocity.
A. 6 m/s
B. 5 m/s
C. 10 m/s
D. 4 m/s
Answer : Option A
Explanation :
If maximum velocity is V.
\(V=a_{1}t_{1}\) and \(V=a_{2}t_{2}\)
\(T=t_{1}+t_{2}=\frac{V}{a_{1}}+\frac{V}{a_{2}}\)
\(V=\frac{a_{1}a_{2}T}{a_{1}+a_{2}}\)
49. The relation between time and displacement of a moving particle is given by \(t=2\alpha x^{2}\) where \(\alpha \) is a constant. The shape of the graph \(x\rightarrow y\) is _____
Here are the graphs of \(x\rightarrow y\) of a moving body. Which of them is not suitable ?
(1).
(2).
(3).
(4).
