The acceleration of a particle starting from rest, varies with time according to the relation A = – 2 sinω t. The displacement of this particle at a time t will be

(1) $-\frac{1}{2}\text{\hspace{0.17em}}\left(a{\omega }^{2}\mathrm{sin}\omega \text{\hspace{0.17em}}t\right)\text{\hspace{0.17em}}{t}^{2}$

(2) $a\omega \text{\hspace{0.17em}}\mathrm{sin}\omega \text{\hspace{0.17em}}t$

(3) $a\omega \text{\hspace{0.17em}}\mathrm{cos}\omega \text{\hspace{0.17em}}t$

(4) $a\text{\hspace{0.17em}}\mathrm{sin}\omega \text{\hspace{0.17em}}t$

Concept Questions :-

Non-uniform acceleration
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If the velocity of a particle is (10 + 2t2) m/s, then the average acceleration of the particle between 2s and 5s is

(1) 2 m/s2

(2) 4 m/s2

(3) 12 m/s2

(4) 14 m/s2

Concept Questions :-

Non-uniform acceleration
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A bullet moving with a velocity of 200 cm/s penetrates a wooden block and comes to rest after traversing 4 cm inside it. What velocity is needed for travelling distance of 9 cm in same block?

1. 100 cm/s

2. 136.2 cm/s

3. 300 cm/s

4. 250 cm/s

Concept Questions :-

Acceleration
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A thief is running away on a straight road in jeep moving with a speed of 9 ms–1. A police man chases him on a motor cycle moving at a speed of 10 ms–1. If the instantaneous separation of the jeep from the motorcycle is 100 m, how long will it take for the police to catch the thief

(1) 1 s

(2) 19 s

(3) 90 s

(4) 100 s

Concept Questions :-

Relative motion in 1-D
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A car A is travelling on a straight level road with a uniform speed of 60 km/h. It is followed by another car B which is moving with a speed of 70 km/h. When the distance between them is 2.5 km, the car B is given a deceleration of 20 km/h2. After how much time will B catch up with A

(1) 1 hr

(2) 1/2 hr

(3) 1/4 hr

(4) 1/8 hr

Concept Questions :-

Acceleration
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The speed of a body moving with uniform acceleration is u. This speed is doubled while covering a distance S. When it covers an additional distance S, its speed would become

(1) $\sqrt{3}\text{\hspace{0.17em}}u$

(2) $\sqrt{5}\text{\hspace{0.17em}}u$

(3) $\sqrt{11}\text{\hspace{0.17em}}u$

(4) $\sqrt{7}\text{\hspace{0.17em}}u$

Concept Questions :-

Uniformly accelerated motion
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Two trains one of length 100 m and another of length 125 m, are moving in mutually opposite directions along parallel lines, meet each other, each with speed 10 m/s. If their acceleration are 0.3 m/s2 and 0.2 m/s2 respectively, then the time they take to pass each other will be

(1) 5 s

(2) 10 s

(3) 15 s

(4) 20 s

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A body starts from rest with uniform acceleration. If its velocity after n second is v, then its displacement in the last two seconds is

(1) $\frac{2v\left(n+1\right)}{n}$

(2) $\frac{v\left(n+1\right)}{n}$

(3) $\frac{v\left(n-1\right)}{n}$

(4) $\frac{2v\left(n-1\right)}{n}$

Concept Questions :-

Acceleration
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A point starts moving in a straight line with a certain acceleration. At a time t after beginning of motion the acceleration suddenly becomes retardation of the same value. The time in which the point returns to the initial point is

(1) $\sqrt{2t}$

(2) $\left(2+\sqrt{2}\right)\text{\hspace{0.17em}}t$

(3) $\frac{t}{\sqrt{2}}$

(4) Cannot be predicted unless acceleration is given

Concept Questions :-

Acceleration
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A particle is moving in a straight line and passes through a point O with a velocity of 6 ms–1. The particle moves with a constant retardation of 2 ms–2 for 4 s and there after moves with constant velocity. How long after leaving O does the particle return to O

(1) 3s

(2) 8s

(3) Never

(4) 4s

Concept Questions :-

Acceleration